Question

In the following exercises, solve by completing the square.

$r^2+6r=-100$

Short answer

The given equation has no solution.

Step-by-step solution

Given information. 

Given equation$r^2+6r=-100$

Make the perfect square.

Add 9 to both sides of the equation.

$$\begin{gathered} r^2+6r+9=-100+9 \\ {r}^2+6r+9=-91 \end{gathered}$$

Writing it as a binomial square.

$$\begin{gathered} r^2+2\times r\times 3+3^2=-91 \\ {(r+3)}^2=-91 \end{gathered}$$

Use the square root property. 

$r+3=\pm \sqrt{-91}$

Because the square root of a negative number is not real, So there is no real solution to the given equation.