Question

In the following exercises, solve.

(a) $\sqrt{s-8}-s=-8$

(b)role="math" localid="1647990991155" $\sqrt{w+25}-w+5=0$

Short answer

Part (a) : $s=8,9$

Part (b) : $w=0,11$

Step-by-step solution

Part (a). Step 1. Given information.

An equation is given as$\sqrt{s-8}-s=-8$.

Part (a) Step 2. Solution.

Isolate radical to one side, take square and simplify.

$$\begin{gathered} \sqrt{s-8}-s=-8 \\ \sqrt{s-8}-s+s=-8+s \\ \sqrt{s-8}=s-8 \\ {\left(\sqrt{s-8}\right)}^2={(s-8)}^{2}s-8=s^2-16s+64 \\ 0=s^2-16s+64-s+8 \\ 0=s^2-17s+72 \\ {s}^2-17s+72=0 \\ {s}^2-9s-8s+72=0 \\ s(s-9)-8(s-9)=0 \\ (s-9)(s-8)=0 \\ s=9ors=8 \end{gathered}$$

Part (b) Step 1. Solution.

To solve $\sqrt{w+25}-w+5=0$.

Isolate radical to one side, take square and simplify.

$$\begin{gathered} \sqrt{w+25}-w+5=0 \\ \sqrt{w+25}-w+5+w-5=0+w-5 \\ \sqrt{w+25}=w-5 \\ {\left(\sqrt{w+25}\right)}^2={(w-5)}^{2}w+25=w^2-10w+25 \\ 0=w^2-10w-w+25-25 \\ 0=w^2-11w \\ {w}^2-11w=0 \\ w(w-11)=0 \\ w=0orw=11 \end{gathered}$$