Q. 326 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{10+2c}=\sqrt{4c+16}$

Step-by-Step Solution

Answer

The solution of the given equation is $c=-3$.

Step 1. Given information.

The given equation is:

$\sqrt{10+2c}=\sqrt{4c+16}$

Step 2. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{10+2c}{)}^2& =& (\sqrt{4c+16}{)}^2\\ 10+2c& =& 4c+16\\ 10-16& =& 4c-2c\\ -6& =& 2c\end{array}$

Divide both sides by 2.

$\begin{array}{rcl}\frac{-6}{2}& =& \frac{2c}{2}\\ -3& =& c\end{array}$

Step 3. Conclusion.

The solution of the given equation is $c=-3$.