Question

Solve the equation by completing square method.

$r^2-6r=-11$

Short answer

The equation has no real solutions.

Step-by-step solution

Given Information  

The Given equation is$r^2-6r=-11$.

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

$r^2-6r=-11$

Here,$b=-6$.

Find 12b2 and add to the both sides of equation.  

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

Add $9$both sides.

$$\begin{gathered} r^2-6r+9=-11+9 \\ {r}^2-6r+9=-2 \end{gathered}$$

Factor the perfect square trinomial as a binomial square.  

$(r-3{)}^2=-2$

Use the square root property.

$r-3=\pm \sqrt{-2}$

Since $\sqrt{-2}$is not a real number.

Thus, the equation has no real solutions.