Solve.
-$$( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0$$
A) $- \frac { 5 } { 4 } , - \frac { 11 } { 4 }$
B) $- \frac { 3 } { 4 } , \frac { 3 } { 4 }$
C) $- \frac { 3 } { 4 } , - \frac { 3 } { 4 }$
D) $\frac { 5 } { 4 } , \frac { 11 } { 4 }$

Question

Quizplus · Accepted Answer

This equation can be solved by recognizing it as a quadratic equation in the form of $(ax + b)^2 + 2c(ax + b) + c^2 = 0$, where $a = 4$, $b = 4$, and $c = 2$. Factoring or using the quadratic formula with the substitution $y = 4m + 4$, we find the roots for $y$, then solve for $m$. The correct roots are $-\frac{5}{4}$ and $-\frac{11}{4}$, corresponding to choice A.

Solve - (4m+4)2+8(4m+4)+7=0( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0(4m+4)2+8(4m+4)+7=0

Solve
- $( 4 m + 4 ) ^ { 2 } + 8 ( 4 m + 4 ) + 7 = 0$