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