Answer
$x=5$ and $x=-4$
Work Step by Step
The given equation is
$\Rightarrow (2x-1)^2=81$
Take the square root of each side.
$\Rightarrow 2x-1=\pm\sqrt {81}$
Simplify.
$\Rightarrow 2x-1=\pm 9$
Add $1$ to each side.
$\Rightarrow 2x-1+1=1\pm 9$
Simplify.
$\Rightarrow 2x=1\pm 9$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{1\pm 9}{2}$
Simplify.
$\Rightarrow x=\frac{1\pm 9}{2}$
Two real solutions are
$\Rightarrow x=\frac{1+9}{2}$ or $x=\frac{1- 9}{2}$
Simplify.
$\Rightarrow x=\frac{10}{2}$ or $x=\frac{-8}{2}$
$\Rightarrow x=5$ or $x=-4$
Hence, the solutions are $x=5$ and $x=-4$.
