Question

In the following exercises, solve by completing the square.

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

Short answer

The solution is$m=-11,m=1$.

Step-by-step solution

Step 1. Given information 

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

Step 2. Calculation   

We have,

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

$3\left(m^2+10m-9\right)=3\left(2\right)$

localid="1645163752120" $\frac{3\left(m^2+10m-9\right)}{3}=\frac{3\left(2\right)}{3}$

localid="1645163853795" $m^2+10m-9=2$

$m^2+10m-9+9=2+9$

$m^2+10m=11$

localid="1645163922467" $m^2+10m+{\left(\frac{1}{2}·\left(10\right)\right)}^2=11+{\left(\frac{1}{2}·\left(10\right)\right)}^2$

localid="1645163946899" $m^2+10m+{\left(5\right)}^2=11+{\left(5\right)}^2$

localid="1645163964764" $m^2+10m+25=11+25$

localid="1645164005576" ${\left(m+5\right)}^2=36$

$\sqrt{{\left(m+5\right)}^2}=\sqrt{36}$

localid="1645164332028" $m+5=\pm 6$

$m+5=-6,m+5=6$

localid="1645164378725" $m+5-5=-6-5,m+5-5=6-5$

localid="1645164386296" $m=-11,m=1$