Q. 336 - Intermediate Algebra

Question

In the following exercises, solve.

$-2=\sqrt{d-20}-\sqrt{d}$

Step-by-Step Solution

Answer

The solution of the given equation is $d=36$.

Step 1. Given information.

The given equation is:

$-2=\sqrt{d-20}-\sqrt{d}$

Step 2. Simplify the equation.

The given equation can be written as:

$\sqrt{d}-2=\sqrt{d-20}$

Take square on both sides.

$\begin{array}{rcl}(\sqrt{d}-2{)}^2& =& (\sqrt{d-20}{)}^2\\ (\sqrt{d}{)}^2-2(\sqrt{d}\left)\right(2)+(2{)}^2& =& d-20\\ d-4\sqrt{d}+4-d+20& =& 0\\ 24-4\sqrt{d}& =& 0\end{array}$

Step 3. Solve the equation.

The above equation can be written as:

$24=4\sqrt{d}$

Divide both sides by 4.

$\begin{array}{rcl}\frac{24}{4}& =& \sqrt{d}\\ 6& =& \sqrt{d}\\ (6{)}^2& =& (\sqrt{d}{)}^2\\ 36& =& d\end{array}$

Step 4. Conclusion.

The solution of the given equation is $d=36$.