Q. 318 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{w+25}-w=-5$

Step-by-Step Solution

Answer

The solution of the given equation is $w=11$.

Step 1. Given information.

The given equation is:

$\sqrt{w+25}-w=-5$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{w+25}=w-5$

Take square on both sides.

$\begin{array}{rcl}w+25& =& (w-5{)}^2\\ w+25& =& w^2-2\left(w\right)\left(5\right)+(5{)}^2\\ 0& =& w^2-10w+25-w-25\\ 0& =& w^2-11w\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$\begin{array}{rcl}{w}^2-11w& =& 0\\ w(w-11)& =& 0\\ w& =& 0,11\end{array}$

For $w=0$,

$\sqrt{0+25}-0=5\ne -5$

For $w=11$,

$\sqrt{11+25}-11=-5$

Step 4. Conclusion.

The solution of the given equation is $w=11$.