Question

Solve the equation by completing square method.$r^2+6r=-100$

Short answer

The required result is no solution

Step-by-step solution

Given Information.   

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

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

$r^2+6r=-100$

The coefficient$r$is$6$

So ,$b=6$

Find 12b2and add to the both sides of equation.

$$\begin{gathered} ={\left(\frac{1}{2}\left(6\right)\right)}^2 \\ ={\left(3\right)}^2 \\ =9 \end{gathered}$$

Add$9$ both side of equation

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

Factor the perfect square trinomial as a binomial square  

${\left(r+3\right)}^2=-91$

$-91\le 0$

Square root property is not applicable

We can not find the solution of this equation