Q. 302 - Intermediate Algebra

Question

In the following exercises, solve.
$\sqrt{v-10}+10=v$

Step-by-Step Solution

Answer

The solutions of the given equation are $v=10$ and $v=11$.

Step 1. Given information.

The given equation is:

$\sqrt{v-10}+10=v$

Step 2. Solve the equation.

The given equation can be written as:

$\sqrt{v-10}=v-10$

Take square on both sides.

$\begin{array}{rcl}(\sqrt{v-10}{)}^2& =& (v-10{)}^2\\ v-10& =& (v-10{)}^2\\ 0& =& (v-10{)}^2-(v-10)\\ 0& =& (v-10)(v-10-1)\\ 0& =& (v-10)(v-11)\\ v& =& 10,11\end{array}$

Step 3. Conclusion.

The solutions of the given equation are $v=10$ and $v=11$.