Q. 317 - Intermediate Algebra

Question

In the following exercises, solve.

$\sqrt{z+100}-z=-10$

Step-by-Step Solution

Answer

The solution of the given equation is $z=21$.

Step 1. Given information.

The given equation is:

$\sqrt{z+100}-z=-10$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{z+100}=z-10$

Take square on both sides.

$\begin{array}{rcl}z+100& =& (z-10{)}^2\\ z+100& =& z^2-2\left(z\right)\left(10\right)+(10{)}^2\\ 0& =& z^2-20z+100-z-100\\ 0& =& z^2-21z\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$\begin{array}{rcl}{z}^2-21z& =& 0\\ z(z-21)& =& 0\\ z& =& 0,21\end{array}$

For $z=0$,

$\sqrt{0+100}-0=10\ne -10$

For $z=21$,

$\sqrt{21+100}-21=-10$

Step 4. Conclusion.

The solution of the given equation is $z=21$.