Answer
$x=-\frac{1}{2}$ and $x=-2$
Work Step by Step
The given equation is
$\Rightarrow (4x+5)^2=9$
Take the square root of each side.
$\Rightarrow 4x+5=\pm\sqrt {9}$
Simplify.
$\Rightarrow 4x+5=\pm 3$
Subtract $5$ from each side.
$\Rightarrow 4x+5-5=-5\pm 3$
Simplify.
$\Rightarrow 4x=-5\pm 3$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{-5\pm 3}{4}$
Simplify.
$\Rightarrow x=\frac{-5\pm 3}{4}$
Two real solutions are
$\Rightarrow x=\frac{-5+3}{4}$ or $x=\frac{-5-3}{4}$
Simplify.
$\Rightarrow x=\frac{-2}{4}$ or $x=\frac{-8}{4}$
$\Rightarrow x=-\frac{1}{2}$ or $x=-2$
Hence, the solutions are $x=-\frac{1}{2}$ and $x=-2$.
