Ten quadratic equations for solving practice.

Actually, there is no image uploaded — you’ve pasted a list of 10 quadratic equations as text. I’ll solve each one step-by-step and explain the method used.

All these are quadratic equations of the form `ax² + bx + c = 0`. We can solve them by:

- Moving all terms to one side to set the equation to zero.
- Simplifying if possible (divide by GCF).
- Factoring (if easy), or using the quadratic formula:
> x = [-b ± √(b² - 4ac)] / (2a)

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Let’s solve each one:

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1.) 10x² + 20x - 71 = 9

→ Subtract 9 from both sides:
10x² + 20x - 80 = 0

Divide entire equation by 10:
x² + 2x - 8 = 0

Factor:
(x + 4)(x - 2) = 0

✔ Solutions: x = -4, x = 2

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2.) x² - 20x + 49 = -2

→ Add 2 to both sides:
x² - 20x + 51 = 0

Try factoring: Look for two numbers that multiply to 51 and add to -20 → -3 and -17.

(x - 3)(x - 17) = 0

✔ Solutions: x = 3, x = 17

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3.) 2x² + 16x - 70 = -4

→ Add 4 to both sides:
2x² + 16x - 66 = 0

Divide by 2:
x² + 8x - 33 = 0

Factor: Numbers that multiply to -33 and add to 8 → 11 and -3.

(x + 11)(x - 3) = 0

✔ Solutions: x = -11, x = 3

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4.) x² + 12x - 20 = 8

→ Subtract 8:
x² + 12x - 28 = 0

Factor: Numbers that multiply to -28 and add to 12 → 14 and -2.

(x + 14)(x - 2) = 0

✔ Solutions: x = -14, x = 2

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5.) x² - 16x + 50 = 2

→ Subtract 2:
x² - 16x + 48 = 0

Factor: Numbers that multiply to 48 and add to -16 → -12 and -4.

(x - 12)(x - 4) = 0

✔ Solutions: x = 12, x = 4

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6.) 10x - 20x - 83 = -3

Wait — this is linear, not quadratic! Let’s check:

Combine like terms:
-10x - 83 = -3

Add 83 to both sides:
-10x = 80

Divide by -10:
✔ Solution: x = -8

*(Note: This was likely a typo — maybe meant 10x²? But as written, it's linear.)*

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7.) x² - 18x - 56 = 7

→ Subtract 7:
x² - 18x - 63 = 0

Factor: Numbers that multiply to -63 and add to -18 → -21 and 3.

(x - 21)(x + 3) = 0

✔ Solutions: x = 21, x = -3

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8.) 3x² - 18x - 42 = 6

→ Subtract 6:
3x² - 18x - 48 = 0

Divide by 3:
x² - 6x - 16 = 0

Factor: Numbers that multiply to -16 and add to -6 → -8 and 2.

(x - 8)(x + 2) = 0

✔ Solutions: x = 8, x = -2

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9.) x² + 4x - 25 = 7

→ Subtract 7:
x² + 4x - 32 = 0

Factor: Numbers that multiply to -32 and add to 4 → 8 and -4.

(x + 8)(x - 4) = 0

✔ Solutions: x = -8, x = 4

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10.) x² - 16x - 20 = -3

→ Add 3 to both sides:
x² - 16x - 17 = 0

Factor: Numbers that multiply to -17 and add to -16 → -17 and 1.

(x - 17)(x + 1) = 0

✔ Solutions: x = 17, x = -1

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## ✔ Final Answers:

1. x = -4, 2
2. x = 3, 17
3. x = -11, 3
4. x = -14, 2
5. x = 12, 4
6. x = -8 *(linear equation)*
7. x = 21, -3
8. x = 8, -2
9. x = -8, 4
10. x = 17, -1

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## 💡 Tips for Solving Quadratics:

- Always move everything to one side to set equal to zero.
- Simplify by dividing by common factors if possible.
- Try factoring first — look for pairs of numbers that multiply to “c” and add to “b”.
- If factoring doesn’t work easily, use the quadratic formula.
- Check your answers by plugging back into the original equation!

Let me know if you’d like to see any solved with the quadratic formula instead!