Question

In the following exercises, solve.
$\sqrt{s-8}=s-8$

Short answer

The solutions of the given equation are $s=8$and $s=9$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$\sqrt{s-8}=s-8$

Step 2. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{s-8}{)}^2& =& (s-8{)}^2\\ s-8& =& (s-8{)}^2\\ 0& =& (s-8{)}^2-(s-8)\\ 0& =& (s-8)(s-8-1)\\ 0& =& (s-8)(s-9)\\ s& =& 8,9\end{array}$

Step 3. Conclusion.

The solutions of the given equation are $s=8$and $s=9$.