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

Question

asked Jan 9, 2023 114k views

1 Answer

Nfelger · Answer 1 · 2023-01-15T19:31:31+0000

The given equation is

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.

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

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