Solving Quadratic Equations (B) - By Factoring Worksheet | Algebra ... - Free Printable

Since the user has not selected any of the options (ExplainAnswer, TeachTopic, GeneratePractice) — all are set to false — and only requested solving the problem accurately, I will proceed to solve Section A as it is the first task presented in the worksheet.

Section A asks:
Write down the values of a, b, and c in each equation, then solve using the quadratic formula. Leave answers to 2 decimal places.

The quadratic formula is:
x = [ -b ± √(b² - 4ac) ] / (2a)

We’ll go one by one.

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Equation 1: x² + 3x - 1 = 0

Standard form: ax² + bx + c = 0
So:
a = 1
b = 3
c = -1

Now plug into formula:

Discriminant D = b² - 4ac = (3)² - 4(1)(-1) = 9 + 4 = 13

√13 ≈ 3.6056

x = [ -3 ± 3.6056 ] / 2

First solution: (-3 + 3.6056)/2 = 0.6056/2 = 0.3028 → 0.30

Second solution: (-3 - 3.6056)/2 = -6.6056/2 = -3.3028 → -3.30

✔ Rounded to 2 decimal places: x = 0.30 or x = -3.30

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Equation 2: 6 - 3x - 2x² = 0

Rewrite in standard order: -2x² - 3x + 6 = 0
But usually we prefer positive leading coefficient? Actually, no — just match coefficients.

So:
a = -2
b = -3
c = 6

Wait — let’s double-check: original is 6 - 3x - 2x² = 0 → rearranged: -2x² -3x +6 = 0 → yes.

Alternatively, multiply entire equation by -1 to make ‘a’ positive: 2x² + 3x - 6 = 0 → this might be easier. But since the question doesn’t specify, either way works as long as consistent.

Let’s use original: a=-2, b=-3, c=6

D = b² - 4ac = (-3)² - 4(-2)(6) = 9 + 48 = 57

√57 ≈ 7.5498

x = [ -(-3) ± 7.5498 ] / (2 * -2) = [3 ± 7.5498] / (-4)

First solution: (3 + 7.5498)/(-4) = 10.5498/-4 = -2.63745 → -2.64

Second solution: (3 - 7.5498)/(-4) = (-4.5498)/(-4) = 1.13745 → 1.14

✔ Answers: x = -2.64 or x = 1.14

*(Note: If we had used 2x² + 3x - 6 = 0 → a=2, b=3, c=-6 → D=9+48=57 → x=(-3±√57)/4 → same results)*

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Equation 3: 8x² - 7 = 0

This is missing the 'x' term → so b = 0

Standard form: 8x² + 0x - 7 = 0

So:
a = 8
b = 0
c = -7

D = 0² - 4(8)(-7) = 0 + 224 = 224

√224 = √(16*14) = 4√14 ≈ 4 * 3.7416 = 14.9664

x = [ -0 ± 14.9664 ] / (2*8) = ±14.9664 / 16

First: 14.9664 / 16 ≈ 0.9354 → 0.94

Second: -14.9664 / 16 ≈ -0.9354 → -0.94

✔ Answers: x = 0.94 or x = -0.94

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Final Answer:
Section A completed:

1) a=1, b=3, c=-1 → x = 0.30, -3.30
2) a=-2, b=-3, c=6 → x = -2.64, 1.14
3) a=8, b=0, c=-7 → x = 0.94, -0.94