Answer
$x=\frac{9}{2}$ and $x=-\frac{1}{2}$
Work Step by Step
The given equation is
$\Rightarrow 4(x-2)^2=25$
Divide each side by $4$.
$\Rightarrow \frac{4(x-2)^2}{4}=\frac{25}{4}$
Simplify.
$\Rightarrow (x-2)^2=\frac{25}{4}$
Take the square root of each side.
$\Rightarrow x-2=\pm\sqrt {\frac{25}{4}}$
Simplify.
$\Rightarrow x-2=\pm\frac{5}{2}$
Add $2$ to each side.
$\Rightarrow x-2+2=2\pm\frac{5}{2}$
Simplify.
$\Rightarrow x=2\pm\frac{5}{2}$
Two real solutions are
$\Rightarrow x=2+\frac{5}{2}$ or $x=2-\frac{5}{2}$
Simplify.
$\Rightarrow x=\frac{9}{2}$ or $x=-\frac{1}{2}$
Hence, the solutions are $x=\frac{9}{2}$ and $x=-\frac{1}{2}$.
