Quadratic Formula Worksheets - Math Monks - Free Printable

Let’s solve each quadratic equation step by step. We’ll use factoring, completing the square, or the quadratic formula as needed. The standard form is:

> ax² + bx + c = 0

And the quadratic formula is:

> x = [−b ± √(b² − 4ac)] / (2a)

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① 10x² − 26x + 12 = 0

First, simplify by dividing all terms by 2:

→ 5x² − 13x + 6 = 0

Now factor:

We need two numbers that multiply to 5×6=30 and add to -13 → -10 and -3

Split middle term:

→ 5x² − 10x − 3x + 6 = 0
→ 5x(x − 2) − 3(x − 2) = 0
→ (5x − 3)(x − 2) = 0

Solutions: x = 3/5, x = 2

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② 3x² + 14x − 49 = 0

Try factoring:

Multiply a×c = 3×(-49) = -147

Need two numbers that multiply to -147 and add to 14 → 21 and -7

Split middle term:

→ 3x² + 21x − 7x − 49 = 0
→ 3x(x + 7) − 7(x + 7) = 0
→ (3x − 7)(x + 7) = 0

Solutions: x = 7/3, x = -7

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③ 2x² + 3x − 20 = 0

Multiply a×c = 2×(-20) = -40

Need two numbers that multiply to -40 and add to 3 → 8 and -5

Split middle term:

→ 2x² + 8x − 5x − 20 = 0
→ 2x(x + 4) − 5(x + 4) = 0
→ (2x − 5)(x + 4) = 0

Solutions: x = 5/2, x = -4

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④ x² + 3x − 4 = 0

Factor directly:

Two numbers: multiply to -4, add to 3 → 4 and -1

→ (x + 4)(x − 1) = 0

Solutions: x = -4, x = 1

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⑤ x² − 9 = 0

This is a difference of squares:

→ (x − 3)(x + 3) = 0

Solutions: x = 3, x = -3

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⑥ x² − 6x − 16 = 0

Factor:

Two numbers: multiply to -16, add to -6 → -8 and 2

→ (x − 8)(x + 2) = 0

Solutions: x = 8, x = -2

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⑦ x² + 6x − 10 = 30

First, bring all terms to one side:

→ x² + 6x − 10 − 30 = 0
→ x² + 6x − 40 = 0

Factor:

Two numbers: multiply to -40, add to 6 → 10 and -4

→ (x + 10)(x − 4) = 0

Solutions: x = -10, x = 4

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⑧ 4x² + 2x − 12 = 0

Simplify by dividing all terms by 2:

→ 2x² + x − 6 = 0

Factor:

Multiply a×c = 2×(-6) = -12

Need two numbers: multiply to -12, add to 1 → 4 and -3

Split middle term:

→ 2x² + 4x − 3x − 6 = 0
→ 2x(x + 2) − 3(x + 2) = 0
→ (2x − 3)(x + 2) = 0

Solutions: x = 3/2, x = -2

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## ✔ Final Answers:

① x = 3/5, 2
② x = 7/3, -7
③ x = 5/2, -4
④ x = -4, 1
⑤ x = -3, 3
⑥ x = -2, 8
⑦ x = -10, 4
⑧ x = -2, 3/2

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Let me know if you’d like to see any solved using the quadratic formula for verification!