Answer:
x = 4
Step-by-step 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