Question

Which quadratic equation is equivalent to (x-2)^2+5(x+2)-6=0

Answer 1

x² + x + 8 = 0

Explanation:

Given

(x - 2)² + 5(x + 2) - 6 = 0 ← expand (x - 2)² and distribute parenthesis by 5

x² - 4x + 4 + 5x + 10 - 6 = 0 ← collect like terms on left side

x² + x + 8 = 0 ← equivalent quadratic equation

Answer 2

x² + x + 8 = 0

Explanation:

(x-2)^2 + 5(x+2) - 6=0 { (a-b)² = a² -2ab + b²; here a = x & b = 2}

x²- 2*x*2 + 2² + 5 x + 10 -6 = 0

x² - 4x + 4 + 5x + 10 - 6 = 0

x² + x + 4 + 10 - 6 = 0

x² + x + 8 = 0