Question

Solve the quadratic equation using square root property.

$2r^2=32$

Short answer

The solutions are$r=\pm 4$.

Step-by-step solution

Given Information.    

The Given equation is $2r^2=32$.

Isolate the quadratic term and makes its coefficient one.   

$$\begin{gathered} r^2=\frac{32}{2} \\ {r}^2=16 \end{gathered}$$

Use the square root property. 

$$\begin{gathered} r=\pm \sqrt{16} \\ r=\pm 4 \end{gathered}$$

Check the solutions.   

Substitute $r=4$

$$\begin{gathered} 2r^2=32 \\ 2\left(4{)}^2\stackrel{?}{=}32 \\ 2\right(16)\stackrel{?}{=}32 \\ 32=32True \end{gathered}$$

Substitute $r=-4$

$$\begin{gathered} 2r^2=32 \\ 2(-4{)}^2\stackrel{?}{=}32 \\ 2(16)\stackrel{?}{=}32 \\ 32=32True \end{gathered}$$

Thus, the solutions are$r=-4,4$.