Find the value of x.
a. 2
b. 4
c. 6
d. 8

Explanation:

Use the Pyhagorean theorem

leg² + leg² = hypotenuse²

We have leg = x, leg = x - 2 and hypotenuse = √20. Substitute:

x² + (x - 2)² = (√20)²

use (a - b)² = a² + 2ab + b² and (√a)² = a

x² + x² - 2(x)(2) + 2² = 20

2x² - 4x + 4 = 20                subtract 20 from both sides

2x² - 4x - 16 = 0              divide both sides by 2

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

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

(x + 2)(x - 4) = 0 ⇔ x + 2 = 0 ∨ x - 4 = 0

x + 2 = 0           subtract 2 from both sides

x = -2 < 0

x - 4 = 0           add 4 to both sides

x = 4

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