Algebra 1 Worksheets - Easy Hard Science - Free Printable

Let’s solve each quadratic equation using the quadratic formula:

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

We’ll go one by one.

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Problem 1: x² + 3x + 2 = 0

Here, a = 1, b = 3, c = 2

Step 1: Calculate discriminant → b² - 4ac
= 3² - 4(1)(2) = 9 - 8 = 1

Step 2: Plug into formula
x = (-3 ± √1) / (2×1) = (-3 ± 1)/2

So two solutions:
x = (-3 + 1)/2 = -2/2 = -1
x = (-3 - 1)/2 = -4/2 = -2

✔ Final answers for this one: x = -1 or x = -2

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Problem 2: x² - 3x + 2 = 0

a = 1, b = -3, c = 2

Discriminant: (-3)² - 4(1)(2) = 9 - 8 = 1

x = (3 ± √1)/2 = (3 ± 1)/2

x = (3+1)/2 = 4/2 = 2
x = (3-1)/2 = 2/2 = 1

✔ Final answers: x = 2 or x = 1

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Problem 3: x² - x - 2 = 0

a = 1, b = -1, c = -2

Discriminant: (-1)² - 4(1)(-2) = 1 + 8 = 9

√9 = 3

x = (1 ± 3)/2

x = (1+3)/2 = 4/2 = 2
x = (1-3)/2 = -2/2 = -1

✔ Final answers: x = 2 or x = -1

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Problem 4: 10x² + 10x - 20 = 0

First, we can simplify by dividing all terms by 10:
→ x² + x - 2 = 0

But let’s use original coefficients to match the work shown:
a = 10, b = 10, c = -20

Discriminant: b² - 4ac = 10² - 4(10)(-20) = 100 + 800 = 900

√900 = 30

x = (-10 ± 30) / (2×10) = (-10 ± 30)/20

Two solutions:
x = (-10 + 30)/20 = 20/20 = 1
x = (-10 - 30)/20 = -40/20 = -2

✔ Final answers: x = 1 or x = -2

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Final Answer:
For x² + 3x + 2 = 0 → x = -1, -2
For x² - 3x + 2 = 0 → x = 1, 2
For x² - x - 2 = 0 → x = -1, 2
For 10x² + 10x - 20 = 0 → x = -2, 1