Free Algebra 1 Worksheets—Printable w/ Answers — Mashup Math - Free Printable

Let’s solve each quadratic equation by factoring. We’ll go one at a time, step by step.

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1.) x² + 3x + 2 = 0

We need two numbers that multiply to 2 and add to 3 → those are 1 and 2.

So:
(x + 1)(x + 2) = 0

Set each factor equal to zero:
x + 1 = 0 → x = -1
x + 2 = 0 → x = -2

✔ Solutions: x = -1, x = -2

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2.) x² + 6x = -8

First, move everything to one side:
x² + 6x + 8 = 0

Find two numbers that multiply to 8 and add to 6 → 2 and 4

So:
(x + 2)(x + 4) = 0

Solutions:
x + 2 = 0 → x = -2
x + 4 = 0 → x = -4

✔ Solutions: x = -2, x = -4

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3.) x² + 24 = -11x

Move all terms to left:
x² + 11x + 24 = 0

Numbers that multiply to 24, add to 11 → 3 and 8

So:
(x + 3)(x + 8) = 0

Solutions:
x = -3, x = -8

✔ Solutions: x = -3, x = -8

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4.) -30 = x² + 11x

Move all to one side:
0 = x² + 11x + 30 → or x² + 11x + 30 = 0

Multiply to 30, add to 11 → 5 and 6

So:
(x + 5)(x + 6) = 0

Solutions:
x = -5, x = -6

✔ Solutions: x = -5, x = -6

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5.) x² + 5x + 9 = 5

Subtract 5 from both sides:
x² + 5x + 4 = 0

Multiply to 4, add to 5 → 1 and 4

So:
(x + 1)(x + 4) = 0

Solutions:
x = -1, x = -4

✔ Solutions: x = -1, x = -4

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6.) 3x² + 10x + 21 = 2x²

Subtract 2x² from both sides:
x² + 10x + 21 = 0

Multiply to 21, add to 10 → 3 and 7

So:
(x + 3)(x + 7) = 0

Solutions:
x = -3, x = -7

✔ Solutions: x = -3, x = -7

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7.) x² - 6x = 10 - 3x

Bring all terms to left:
x² - 6x + 3x - 10 = 0 → x² - 3x - 10 = 0

Multiply to -10, add to -3 → -5 and 2

So:
(x - 5)(x + 2) = 0

Solutions:
x = 5, x = -2

✔ Solutions: x = 5, x = -2

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8.) 225 - x² = 0

Rewrite as:
-x² + 225 = 0 → or x² = 225

Take square root:
x = ±√225 → x = ±15

But since we’re factoring:
225 - x² = (15 - x)(15 + x) = 0

So:
15 - x = 0 → x = 15
15 + x = 0 → x = -15

✔ Solutions: x = 15, x = -15

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9.) 2x² + 11x - 7 = x² + 5x

Subtract right side from both sides:
2x² + 11x - 7 - x² - 5x = 0 → x² + 6x - 7 = 0

Multiply to -7, add to 6 → 7 and -1

So:
(x + 7)(x - 1) = 0

Solutions:
x = -7, x = 1

✔ Solutions: x = -7, x = 1

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10.) 14 = 50 + 15x + x²

Move all to left:
0 = x² + 15x + 50 - 14 → x² + 15x + 36 = 0

Multiply to 36, add to 15 → 3 and 12

So:
(x + 3)(x + 12) = 0

Solutions:
x = -3, x = -12

✔ Solutions: x = -3, x = -12

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11.) x² + 9 = 6x + 1

Move all to left:
x² - 6x + 8 = 0

Multiply to 8, add to -6 → -2 and -4

So:
(x - 2)(x - 4) = 0

Solutions:
x = 2, x = 4

✔ Solutions: x = 2, x = 4

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12.) x² = 49

Subtract 49:
x² - 49 = 0 → difference of squares

Factor:
(x - 7)(x + 7) = 0

Solutions:
x = 7, x = -7

✔ Solutions: x = 7, x = -7

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13.) x² - 9x + 18 = 0

Multiply to 18, add to -9 → -3 and -6

So:
(x - 3)(x - 6) = 0

Solutions:
x = 3, x = 6

✔ Solutions: x = 3, x = 6

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14.) x² = -(5x + 4)

Distribute the negative:
x² = -5x - 4

Move all to left:
x² + 5x + 4 = 0

Multiply to 4, add to 5 → 1 and 4

So:
(x + 1)(x + 4) = 0

Solutions:
x = -1, x = -4

✔ Solutions: x = -1, x = -4

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Final Answer:
1.) x = -1, -2
2.) x = -2, -4
3.) x = -3, -8
4.) x = -5, -6
5.) x = -1, -4
6.) x = -3, -7
7.) x = 5, -2
8.) x = 15, -15
9.) x = -7, 1
10.) x = -3, -12
11.) x = 2, 4
12.) x = 7, -7
13.) x = 3, 6
14.) x = -1, -4