Question

Complete the square to the problem X^2+6x-16=0

Answer 1

x = -8 or x = 2

Explanation:

`(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_((*))=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm√(25)\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}`