Solve the equation. $5 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 32$
A) $2 \pm 2 \times \sqrt { 2 } ( - 0.8,4.8 )$
B) $- 2 + 2 \sqrt { 2 } ( 0.8 )$
C) $2 - 2 \sqrt { 2 } ( 4.8 )$
D) $- 2 \pm 2 \sqrt { 2 } ( - 4.8,0.8 )$
E) $- 2 - 2 \sqrt { 2 } ( - 4.8 )$

Question

Quizplus · Accepted Answer

First, simplify the equation: $5(x+2)^2 = (x+2)^2 + 32$. Subtract $(x+2)^2$ from both sides to get $4(x+2)^2 = 32$. Divide by 4 to get $(x+2)^2 = 8$. Taking the square root gives $x+2 = \pm \sqrt{8} = \pm 2\sqrt{2}$. Solving for $x$, we get $x = -2 \pm 2\sqrt{2}$, which corresponds to choice D.

Solve the Equation 5(x+2)2=(x+2)2+325 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 325(x+2)2=(x+2)2+32

Solve the Equation $5 ( x + 2 ) ^ { 2 } = ( x + 2 ) ^ { 2 } + 32$