Question

Solve the equation by completing square method.

$3m^2+30m-27=6$

Short answer

The solutions are$m=-11,m=1$.

Step-by-step solution

Given Information      

The Given equation is $3m^2+30m-27=6$.

Factor out the greatest common factor and divide both sides to isolate the trinomial.

The GCF is $3$.

Divide both sides by $3$.

$$\begin{gathered} \frac{1}{3}(3m^2+30m-27)=\frac{6}{3} \\ {m}^2+10m-9=2 \end{gathered}$$

Simplify.

$$\begin{gathered} m^2+10m=2+9 \\ {m}^2+10m=11 \end{gathered}$$

Add ${\left(\frac{1}{2}\times 10\right)}^2$both sides.

$$\begin{gathered} m^2+10m+25=11+25 \\ {m}^2+10m+25=36 \end{gathered}$$

Factor the perfect square trinomial as a binomial square.  

$(m+5{)}^2=36$

Use the square root property.

$$\begin{gathered} m+5=\pm \sqrt{36} \\ m+5=\pm 6 \end{gathered}$$

Solve for m.

$m=-5\pm 6$

Rewrite to show two solutions.

$$\begin{gathered} m=-5+6=1 \\ m=-5-6=-11 \end{gathered}$$

Thus, the solutions are$m=-11,m=1$.