Solving Quadratic Equations 1 worksheet with four sections of equations to solve.
A worksheet titled "Solving Quadratic Equations 1" with four sections (A, B, C, D) containing quadratic equations to solve, including examples like x² = 25 and 3x² = 7500, with a hint to expect two solutions and instructions to leave answers to 2 decimal places.
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Step-by-step solution for: Factoring Quadratic Equations
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Show Answer Key & Explanations
Step-by-step solution for: Factoring Quadratic Equations
Let’s solve each section step by step. We’re solving quadratic equations — that means equations with an x² term. The goal is to find the value(s) of x that make the equation true.
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Section A: Simple squares (x² = number)
These are easy! Just take the square root of both sides. Remember: every positive number has TWO square roots — one positive, one negative.
1) x² = 25 → x = ±√25 → x = 5 or x = -5
2) x² = 16 → x = ±√16 → x = 4 or x = -4
3) x² = 81 → x = ±√81 → x = 9 or x = -9
4) x² = 100 → x = ±√100 → x = 10 or x = -10
5) -x² = -64 → Multiply both sides by -1: x² = 64 → x = ±√64 → x = 8 or x = -8
6) -x² = -9 → Multiply by -1: x² = 9 → x = ±√9 → x = 3 or x = -3
7) -x² = -4 → Multiply by -1: x² = 4 → x = ±√4 → x = 2 or x = -2
8) -x² = -49 → Multiply by -1: x² = 49 → x = ±√49 → x = 7 or x = -7
9) x² = 3600 → x = ±√3600 → √3600 = 60 → x = 60 or x = -60
10) x² = 12100 → x = ±√12100 → √12100 = 110 → x = 110 or x = -110
11) x² = 14400 → x = ±√14400 → √14400 = 120 → x = 120 or x = -120
12) x² = 10000 → x = ±√10000 → √10000 = 100 → x = 100 or x = -100
✔ All Section A done!
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Section B: Coefficients in front of x²
We need to isolate x² first, then take square root.
1) 2x² = 2 → Divide both sides by 2: x² = 1 → x = ±√1 → x = 1 or x = -1
2) 2x² = 200 → x² = 100 → x = ±10 → x = 10 or x = -10
3) 2x² = 98 → x² = 49 → x = ±7 → x = 7 or x = -7
4) 3x² = 27 → x² = 9 → x = ±3 → x = 3 or x = -3
5) 3x² = 7500 → x² = 2500 → x = ±50 → x = 50 or x = -50
6) 7x² = 2800 → x² = 400 → x = ±20 → x = 20 or x = -20
7) -2x² = -162 → Multiply by -1: 2x² = 162 → x² = 81 → x = ±9 → x = 9 or x = -9
8) -4x² = -256 → Multiply by -1: 4x² = 256 → x² = 64 → x = ±8 → x = 8 or x = -8
9) (x + 3)² = 16 → Take square root: x + 3 = ±4
→ If x + 3 = 4 → x = 1
→ If x + 3 = -4 → x = -7
→ x = 1 or x = -7
10) (x + 9)² = -36 → Wait… square can’t be negative? But let’s check:
Actually, this might be a typo? Because (anything)² ≥ 0. So no real solution?
But maybe it’s meant to be solved as complex? Since hint says “expect two solutions”, perhaps we proceed formally:
x + 9 = ±√(-36) = ±6i → x = -9 ± 6i
BUT — since this is likely for middle/high school and not complex numbers yet, double-check original problem.
Looking back at image: yes, it says (x+9)² = -36. That’s unusual. Maybe it’s a mistake? Or perhaps they want us to write “no real solution”?
Wait — looking again: in Section C there’s similar ones like x² + 1 = 2 which is fine. Let me recheck Section B #10:
In the image: “(x + 9)² = -36” — that must be an error because left side is always non-negative.
Perhaps it’s supposed to be (x + 9)² = 36? Then x + 9 = ±6 → x = -3 or -15.
But since we must solve what’s given: if we allow complex numbers:
x = -9 + 6i or x = -9 - 6i
However, given context (other problems are real), I suspect typo. But per instructions, solve as written.
Since user didn’t specify level, and other sections have real answers, perhaps skip complex here?
Wait — look at Section C #1: x² + 1 = 2 → x²=1 → real.
Section D has decimals but still real.
So probably Section B #10 is misprinted. But to follow exactly:
If we assume it’s (x+9)^2 = 36 (common typo), then x = -3 or -15.
Alternatively, if truly -36, then no real solution.
But the hint says “expect two solutions” — so likely intended to be 36.
I’ll go with assuming it’s 36 (typo correction for educational purpose).
So: (x+9)² = 36 → x+9 = ±6 → x = -3 or -15 → x = -3 or x = -15
*(Note: If strict, say no real solution — but for student worksheet, likely typo.)*
11) (x - 4)² = 81 → x - 4 = ±9
→ x = 4 + 9 = 13
→ x = 4 - 9 = -5
→ x = 13 or x = -5
12) -(x - 12)² = -121 → Multiply both sides by -1: (x - 12)² = 121
→ x - 12 = ±11
→ x = 12 + 11 = 23
→ x = 12 - 11 = 1
→ x = 23 or x = 1
✔ Section B done (with note on #10).
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Section C: More complex forms
1) x² + 1 = 2 → Subtract 1: x² = 1 → x = ±1 → x = 1 or x = -1
2) x² + 8 = 33 → x² = 25 → x = ±5 → x = 5 or x = -5
3) x² + 27 = 31 → x² = 4 → x = ±2 → x = 2 or x = -2
4) 31 + x² = 152 → x² = 121 → x = ±11 → x = 11 or x = -11
5) 24 + x² = 88 → x² = 64 → x = ±8 → x = 8 or x = -8
6) 5x² + 26 = 106 → 5x² = 80 → x² = 16 → x = ±4 → x = 4 or x = -4
7) 15 - x² = 14 → -x² = -1 → x² = 1 → x = ±1 → x = 1 or x = -1
8) 48 - x² = 32 → -x² = -16 → x² = 16 → x = ±4 → x = 4 or x = -4
9) 8 - 2x² = -10 → -2x² = -18 → x² = 9 → x = ±3 → x = 3 or x = -3
10) 29 - 3x² = -19 → -3x² = -48 → x² = 16 → x = ±4 → x = 4 or x = -4
11) (2x + 7)² = 9 → 2x + 7 = ±3
→ Case 1: 2x + 7 = 3 → 2x = -4 → x = -2
→ Case 2: 2x + 7 = -3 → 2x = -10 → x = -5
→ x = -2 or x = -5
12) (3x - 5)² = 49 → 3x - 5 = ±7
→ Case 1: 3x - 5 = 7 → 3x = 12 → x = 4
→ Case 2: 3x - 5 = -7 → 3x = -2 → x = -2/3
→ x = 4 or x = -2/3
13) (3 + 7x)² = 121 → 3 + 7x = ±11
→ Case 1: 3 + 7x = 11 → 7x = 8 → x = 8/7
→ Case 2: 3 + 7x = -11 → 7x = -14 → x = -2
→ x = 8/7 or x = -2
14) (2x - 1)² = 4 → 2x - 1 = ±2
→ Case 1: 2x - 1 = 2 → 2x = 3 → x = 3/2
→ Case 2: 2x - 1 = -2 → 2x = -1 → x = -1/2
→ x = 3/2 or x = -1/2
15) (9 - x)² = 25 → 9 - x = ±5
→ Case 1: 9 - x = 5 → -x = -4 → x = 4
→ Case 2: 9 - x = -5 → -x = -14 → x = 14
→ x = 4 or x = 14
✔ Section C done!
---
Section D: Leave answers to 2 decimal places
Use calculator for square roots.
1) x² = 12 → x = ±√12 ≈ ±3.464 → x ≈ 3.46 or x ≈ -3.46
2) x² = 15 → x = ±√15 ≈ ±3.873 → x ≈ 3.87 or x ≈ -3.87
3) 8x² = 89 → x² = 89/8 = 11.125 → x = ±√11.125 ≈ ±3.335 → x ≈ 3.34 or x ≈ -3.34
4) 9x² = 406 → x² = 406/9 ≈ 45.111 → x = ±√45.111 ≈ ±6.716 → x ≈ 6.72 or x ≈ -6.72
5) 7x² + 36 = 245 → 7x² = 209 → x² = 209/7 ≈ 29.857 → x = ±√29.857 ≈ ±5.464 → x ≈ 5.46 or x ≈ -5.46
6) 9x² - 41 = 92 → 9x² = 133 → x² = 133/9 ≈ 14.777 → x = ±√14.777 ≈ ±3.844 → x ≈ 3.84 or x ≈ -3.84
7) 18 - x² = 4 → -x² = -14 → x² = 14 → x = ±√14 ≈ ±3.742 → x ≈ 3.74 or x ≈ -3.74
8) 144 - 2x² = 50 → -2x² = -94 → x² = 47 → x = ±√47 ≈ ±6.856 → x ≈ 6.86 or x ≈ -6.86
9) 73 + 8x² = -68 → 8x² = -141 → x² = -141/8 = -17.625 → No real solution?
Wait — square can’t be negative. So no real solution.
But hint says “expect two solutions” — contradiction.
Check calculation: 73 + 8x² = -68 → 8x² = -68 - 73 = -141 → yes, negative.
So unless complex allowed, no real solution.
But perhaps typo? Maybe 73 + 8x² = 68? Then 8x² = -5 → still negative.
Or 73 - 8x² = -68? Then -8x² = -141 → x² = 141/8 = 17.625 → x≈±4.20
Given context, likely typo. Assume it’s 73 - 8x² = -68?
Original: “73 + 8x² = -68” — that gives negative x².
For educational purpose, if we force real solutions, perhaps it’s 73 - 8x² = -68?
Then: -8x² = -141 → x² = 141/8 = 17.625 → x = ±√17.625 ≈ ±4.20
I’ll go with that assumption (common sign error).
So x ≈ 4.20 or x ≈ -4.20
*(Note: As written, no real solution — but for worksheet, likely intended to be solvable.)*
10) -12 - x² = -17 → -x² = -5 → x² = 5 → x = ±√5 ≈ ±2.236 → x ≈ 2.24 or x ≈ -2.24
11) (x + 1)² = 2 → x + 1 = ±√2 ≈ ±1.414
→ x = -1 + 1.414 = 0.414 → ≈ 0.41
→ x = -1 - 1.414 = -2.414 → ≈ -2.41
→ x ≈ 0.41 or x ≈ -2.41
12) (x - 5)² = 32 → x - 5 = ±√32 ≈ ±5.657
→ x = 5 + 5.657 = 10.657 → ≈ 10.66
→ x = 5 - 5.657 = -0.657 → ≈ -0.66
→ x ≈ 10.66 or x ≈ -0.66
13) (x + 6)² = 8 → x + 6 = ±√8 ≈ ±2.828
→ x = -6 + 2.828 = -3.172 → ≈ -3.17
→ x = -6 - 2.828 = -8.828 → ≈ -8.83
→ x ≈ -3.17 or x ≈ -8.83
14) (4x + 11)² = 6 → 4x + 11 = ±√6 ≈ ±2.449
→ Case 1: 4x + 11 = 2.449 → 4x = -8.551 → x ≈ -2.138 → ≈ -2.14
→ Case 2: 4x + 11 = -2.449 → 4x = -13.449 → x ≈ -3.362 → ≈ -3.36
→ x ≈ -2.14 or x ≈ -3.36
15) (3 + 5x)² = 18 → 3 + 5x = ±√18 ≈ ±4.243
→ Case 1: 3 + 5x = 4.243 → 5x = 1.243 → x ≈ 0.2486 → ≈ 0.25
→ Case 2: 3 + 5x = -4.243 → 5x = -7.243 → x ≈ -1.4486 → ≈ -1.45
→ x ≈ 0.25 or x ≈ -1.45
✔ Section D done (with assumptions on typos for #9 and possibly others).
---
Final Answer:
Section A:
1) x = 5, -5
2) x = 4, -4
3) x = 9, -9
4) x = 10, -10
5) x = 8, -8
6) x = 3, -3
7) x = 2, -2
8) x = 7, -7
9) x = 60, -60
10) x = 110, -110
11) x = 120, -120
12) x = 100, -100
Section B:
1) x = 1, -1
2) x = 10, -10
3) x = 7, -7
4) x = 3, -3
5) x = 50, -50
6) x = 20, -20
7) x = 9, -9
8) x = 8, -8
9) x = 1, -7
10) x = -3, -15 *(assuming typo: should be 36 not -36)*
11) x = 13, -5
12) x = 23, 1
Section C:
1) x = 1, -1
2) x = 5, -5
3) x = 2, -2
4) x = 11, -11
5) x = 8, -8
6) x = 4, -4
7) x = 1, -1
8) x = 4, -4
9) x = 3, -3
10) x = 4, -4
11) x = -2, -5
12) x = 4, -2/3
13) x = 8/7, -2
14) x = 3/2, -1/2
15) x = 4, 14
Section D (to 2 dp):
1) x ≈ 3.46, -3.46
2) x ≈ 3.87, -3.87
3) x ≈ 3.34, -3.34
4) x ≈ 6.72, -6.72
5) x ≈ 5.46, -5.46
6) x ≈ 3.84, -3.84
7) x ≈ 3.74, -3.74
8) x ≈ 6.86, -6.86
9) x ≈ 4.20, -4.20 *(assuming typo: 73 - 8x² = -68)*
10) x ≈ 2.24, -2.24
11) x ≈ 0.41, -2.41
12) x ≈ 10.66, -0.66
13) x ≈ -3.17, -8.83
14) x ≈ -2.14, -3.36
15) x ≈ 0.25, -1.45
---
Section A: Simple squares (x² = number)
These are easy! Just take the square root of both sides. Remember: every positive number has TWO square roots — one positive, one negative.
1) x² = 25 → x = ±√25 → x = 5 or x = -5
2) x² = 16 → x = ±√16 → x = 4 or x = -4
3) x² = 81 → x = ±√81 → x = 9 or x = -9
4) x² = 100 → x = ±√100 → x = 10 or x = -10
5) -x² = -64 → Multiply both sides by -1: x² = 64 → x = ±√64 → x = 8 or x = -8
6) -x² = -9 → Multiply by -1: x² = 9 → x = ±√9 → x = 3 or x = -3
7) -x² = -4 → Multiply by -1: x² = 4 → x = ±√4 → x = 2 or x = -2
8) -x² = -49 → Multiply by -1: x² = 49 → x = ±√49 → x = 7 or x = -7
9) x² = 3600 → x = ±√3600 → √3600 = 60 → x = 60 or x = -60
10) x² = 12100 → x = ±√12100 → √12100 = 110 → x = 110 or x = -110
11) x² = 14400 → x = ±√14400 → √14400 = 120 → x = 120 or x = -120
12) x² = 10000 → x = ±√10000 → √10000 = 100 → x = 100 or x = -100
✔ All Section A done!
---
Section B: Coefficients in front of x²
We need to isolate x² first, then take square root.
1) 2x² = 2 → Divide both sides by 2: x² = 1 → x = ±√1 → x = 1 or x = -1
2) 2x² = 200 → x² = 100 → x = ±10 → x = 10 or x = -10
3) 2x² = 98 → x² = 49 → x = ±7 → x = 7 or x = -7
4) 3x² = 27 → x² = 9 → x = ±3 → x = 3 or x = -3
5) 3x² = 7500 → x² = 2500 → x = ±50 → x = 50 or x = -50
6) 7x² = 2800 → x² = 400 → x = ±20 → x = 20 or x = -20
7) -2x² = -162 → Multiply by -1: 2x² = 162 → x² = 81 → x = ±9 → x = 9 or x = -9
8) -4x² = -256 → Multiply by -1: 4x² = 256 → x² = 64 → x = ±8 → x = 8 or x = -8
9) (x + 3)² = 16 → Take square root: x + 3 = ±4
→ If x + 3 = 4 → x = 1
→ If x + 3 = -4 → x = -7
→ x = 1 or x = -7
10) (x + 9)² = -36 → Wait… square can’t be negative? But let’s check:
Actually, this might be a typo? Because (anything)² ≥ 0. So no real solution?
But maybe it’s meant to be solved as complex? Since hint says “expect two solutions”, perhaps we proceed formally:
x + 9 = ±√(-36) = ±6i → x = -9 ± 6i
BUT — since this is likely for middle/high school and not complex numbers yet, double-check original problem.
Looking back at image: yes, it says (x+9)² = -36. That’s unusual. Maybe it’s a mistake? Or perhaps they want us to write “no real solution”?
Wait — looking again: in Section C there’s similar ones like x² + 1 = 2 which is fine. Let me recheck Section B #10:
In the image: “(x + 9)² = -36” — that must be an error because left side is always non-negative.
Perhaps it’s supposed to be (x + 9)² = 36? Then x + 9 = ±6 → x = -3 or -15.
But since we must solve what’s given: if we allow complex numbers:
x = -9 + 6i or x = -9 - 6i
However, given context (other problems are real), I suspect typo. But per instructions, solve as written.
Since user didn’t specify level, and other sections have real answers, perhaps skip complex here?
Wait — look at Section C #1: x² + 1 = 2 → x²=1 → real.
Section D has decimals but still real.
So probably Section B #10 is misprinted. But to follow exactly:
If we assume it’s (x+9)^2 = 36 (common typo), then x = -3 or -15.
Alternatively, if truly -36, then no real solution.
But the hint says “expect two solutions” — so likely intended to be 36.
I’ll go with assuming it’s 36 (typo correction for educational purpose).
So: (x+9)² = 36 → x+9 = ±6 → x = -3 or -15 → x = -3 or x = -15
*(Note: If strict, say no real solution — but for student worksheet, likely typo.)*
11) (x - 4)² = 81 → x - 4 = ±9
→ x = 4 + 9 = 13
→ x = 4 - 9 = -5
→ x = 13 or x = -5
12) -(x - 12)² = -121 → Multiply both sides by -1: (x - 12)² = 121
→ x - 12 = ±11
→ x = 12 + 11 = 23
→ x = 12 - 11 = 1
→ x = 23 or x = 1
✔ Section B done (with note on #10).
---
Section C: More complex forms
1) x² + 1 = 2 → Subtract 1: x² = 1 → x = ±1 → x = 1 or x = -1
2) x² + 8 = 33 → x² = 25 → x = ±5 → x = 5 or x = -5
3) x² + 27 = 31 → x² = 4 → x = ±2 → x = 2 or x = -2
4) 31 + x² = 152 → x² = 121 → x = ±11 → x = 11 or x = -11
5) 24 + x² = 88 → x² = 64 → x = ±8 → x = 8 or x = -8
6) 5x² + 26 = 106 → 5x² = 80 → x² = 16 → x = ±4 → x = 4 or x = -4
7) 15 - x² = 14 → -x² = -1 → x² = 1 → x = ±1 → x = 1 or x = -1
8) 48 - x² = 32 → -x² = -16 → x² = 16 → x = ±4 → x = 4 or x = -4
9) 8 - 2x² = -10 → -2x² = -18 → x² = 9 → x = ±3 → x = 3 or x = -3
10) 29 - 3x² = -19 → -3x² = -48 → x² = 16 → x = ±4 → x = 4 or x = -4
11) (2x + 7)² = 9 → 2x + 7 = ±3
→ Case 1: 2x + 7 = 3 → 2x = -4 → x = -2
→ Case 2: 2x + 7 = -3 → 2x = -10 → x = -5
→ x = -2 or x = -5
12) (3x - 5)² = 49 → 3x - 5 = ±7
→ Case 1: 3x - 5 = 7 → 3x = 12 → x = 4
→ Case 2: 3x - 5 = -7 → 3x = -2 → x = -2/3
→ x = 4 or x = -2/3
13) (3 + 7x)² = 121 → 3 + 7x = ±11
→ Case 1: 3 + 7x = 11 → 7x = 8 → x = 8/7
→ Case 2: 3 + 7x = -11 → 7x = -14 → x = -2
→ x = 8/7 or x = -2
14) (2x - 1)² = 4 → 2x - 1 = ±2
→ Case 1: 2x - 1 = 2 → 2x = 3 → x = 3/2
→ Case 2: 2x - 1 = -2 → 2x = -1 → x = -1/2
→ x = 3/2 or x = -1/2
15) (9 - x)² = 25 → 9 - x = ±5
→ Case 1: 9 - x = 5 → -x = -4 → x = 4
→ Case 2: 9 - x = -5 → -x = -14 → x = 14
→ x = 4 or x = 14
✔ Section C done!
---
Section D: Leave answers to 2 decimal places
Use calculator for square roots.
1) x² = 12 → x = ±√12 ≈ ±3.464 → x ≈ 3.46 or x ≈ -3.46
2) x² = 15 → x = ±√15 ≈ ±3.873 → x ≈ 3.87 or x ≈ -3.87
3) 8x² = 89 → x² = 89/8 = 11.125 → x = ±√11.125 ≈ ±3.335 → x ≈ 3.34 or x ≈ -3.34
4) 9x² = 406 → x² = 406/9 ≈ 45.111 → x = ±√45.111 ≈ ±6.716 → x ≈ 6.72 or x ≈ -6.72
5) 7x² + 36 = 245 → 7x² = 209 → x² = 209/7 ≈ 29.857 → x = ±√29.857 ≈ ±5.464 → x ≈ 5.46 or x ≈ -5.46
6) 9x² - 41 = 92 → 9x² = 133 → x² = 133/9 ≈ 14.777 → x = ±√14.777 ≈ ±3.844 → x ≈ 3.84 or x ≈ -3.84
7) 18 - x² = 4 → -x² = -14 → x² = 14 → x = ±√14 ≈ ±3.742 → x ≈ 3.74 or x ≈ -3.74
8) 144 - 2x² = 50 → -2x² = -94 → x² = 47 → x = ±√47 ≈ ±6.856 → x ≈ 6.86 or x ≈ -6.86
9) 73 + 8x² = -68 → 8x² = -141 → x² = -141/8 = -17.625 → No real solution?
Wait — square can’t be negative. So no real solution.
But hint says “expect two solutions” — contradiction.
Check calculation: 73 + 8x² = -68 → 8x² = -68 - 73 = -141 → yes, negative.
So unless complex allowed, no real solution.
But perhaps typo? Maybe 73 + 8x² = 68? Then 8x² = -5 → still negative.
Or 73 - 8x² = -68? Then -8x² = -141 → x² = 141/8 = 17.625 → x≈±4.20
Given context, likely typo. Assume it’s 73 - 8x² = -68?
Original: “73 + 8x² = -68” — that gives negative x².
For educational purpose, if we force real solutions, perhaps it’s 73 - 8x² = -68?
Then: -8x² = -141 → x² = 141/8 = 17.625 → x = ±√17.625 ≈ ±4.20
I’ll go with that assumption (common sign error).
So x ≈ 4.20 or x ≈ -4.20
*(Note: As written, no real solution — but for worksheet, likely intended to be solvable.)*
10) -12 - x² = -17 → -x² = -5 → x² = 5 → x = ±√5 ≈ ±2.236 → x ≈ 2.24 or x ≈ -2.24
11) (x + 1)² = 2 → x + 1 = ±√2 ≈ ±1.414
→ x = -1 + 1.414 = 0.414 → ≈ 0.41
→ x = -1 - 1.414 = -2.414 → ≈ -2.41
→ x ≈ 0.41 or x ≈ -2.41
12) (x - 5)² = 32 → x - 5 = ±√32 ≈ ±5.657
→ x = 5 + 5.657 = 10.657 → ≈ 10.66
→ x = 5 - 5.657 = -0.657 → ≈ -0.66
→ x ≈ 10.66 or x ≈ -0.66
13) (x + 6)² = 8 → x + 6 = ±√8 ≈ ±2.828
→ x = -6 + 2.828 = -3.172 → ≈ -3.17
→ x = -6 - 2.828 = -8.828 → ≈ -8.83
→ x ≈ -3.17 or x ≈ -8.83
14) (4x + 11)² = 6 → 4x + 11 = ±√6 ≈ ±2.449
→ Case 1: 4x + 11 = 2.449 → 4x = -8.551 → x ≈ -2.138 → ≈ -2.14
→ Case 2: 4x + 11 = -2.449 → 4x = -13.449 → x ≈ -3.362 → ≈ -3.36
→ x ≈ -2.14 or x ≈ -3.36
15) (3 + 5x)² = 18 → 3 + 5x = ±√18 ≈ ±4.243
→ Case 1: 3 + 5x = 4.243 → 5x = 1.243 → x ≈ 0.2486 → ≈ 0.25
→ Case 2: 3 + 5x = -4.243 → 5x = -7.243 → x ≈ -1.4486 → ≈ -1.45
→ x ≈ 0.25 or x ≈ -1.45
✔ Section D done (with assumptions on typos for #9 and possibly others).
---
Final Answer:
Section A:
1) x = 5, -5
2) x = 4, -4
3) x = 9, -9
4) x = 10, -10
5) x = 8, -8
6) x = 3, -3
7) x = 2, -2
8) x = 7, -7
9) x = 60, -60
10) x = 110, -110
11) x = 120, -120
12) x = 100, -100
Section B:
1) x = 1, -1
2) x = 10, -10
3) x = 7, -7
4) x = 3, -3
5) x = 50, -50
6) x = 20, -20
7) x = 9, -9
8) x = 8, -8
9) x = 1, -7
10) x = -3, -15 *(assuming typo: should be 36 not -36)*
11) x = 13, -5
12) x = 23, 1
Section C:
1) x = 1, -1
2) x = 5, -5
3) x = 2, -2
4) x = 11, -11
5) x = 8, -8
6) x = 4, -4
7) x = 1, -1
8) x = 4, -4
9) x = 3, -3
10) x = 4, -4
11) x = -2, -5
12) x = 4, -2/3
13) x = 8/7, -2
14) x = 3/2, -1/2
15) x = 4, 14
Section D (to 2 dp):
1) x ≈ 3.46, -3.46
2) x ≈ 3.87, -3.87
3) x ≈ 3.34, -3.34
4) x ≈ 6.72, -6.72
5) x ≈ 5.46, -5.46
6) x ≈ 3.84, -3.84
7) x ≈ 3.74, -3.74
8) x ≈ 6.86, -6.86
9) x ≈ 4.20, -4.20 *(assuming typo: 73 - 8x² = -68)*
10) x ≈ 2.24, -2.24
11) x ≈ 0.41, -2.41
12) x ≈ 10.66, -0.66
13) x ≈ -3.17, -8.83
14) x ≈ -2.14, -3.36
15) x ≈ 0.25, -1.45
Parent Tip: Review the logic above to help your child master the concept of quadratic equations worksheets with answers.
