Question

Solve 1/2r^2-10=3/2r^2 using square roots. Select the solution(s).

Answer 1

The given equation is

`(1)/(2)r^2-10=(3)/(2)r^2`

First, we subtract 3/2 of square r on each side.

`\begin{gathered} (1)/(2)r^2-(3)/(2)r^2-10=(3)/(2)r^2-(3)/(2)r^2 \\ (1-3)/(2)r^2-10=0 \\ -(2)/(2)r^2-10=0 \\ -r^2-10=0 \end{gathered}`

Then, we add 10 on each side.

`\begin{gathered} -r^2-10+10=10 \\ -r^2=10 \end{gathered}`

We multiply the equation by -1.

`\begin{gathered} (-1)\cdot(-r^2)=10\cdot(-1) \\ r^2=-10 \end{gathered}`

At last, we apply the square root on each side.

`\begin{gathered} \sqrt[]{r^2}=\sqrt[]{-10} \\ r=\pm\sqrt[]{-10} \end{gathered}`

Therefore, the solutions are

`\begin{gathered} r_1=\sqrt[]{-10} \\ r_2=-\sqrt[]{-10} \end{gathered}`