Question

In the following exercises, solve using the Square Root Property.

$r^2+32=0$

Short answer

The resultant equation has no real solution.

Step-by-step solution

Step 1. Given information.

The given quadratic equation is:

$r^2+32=0$

Step 2. Solve using the quadratic equation by using Square Root Property.

$r^2+32=0$

Isolate the quadratic term and make its coefficient one by subtracting 32 from both sides,

$$\begin{gathered} r^2+32-32=0-32 \\ {r}^2=-32 \end{gathered}$$

Use Square Root Property,

$r=\pm \sqrt{-32}$

The number $\sqrt{-32}$is not a real number.

Therefore there is no real solution.