Answer
$g\approx 6.65$ and $g\approx 1.35$.
Work Step by Step
The given equation is
$\Rightarrow 3g^2-24g+27=0$
Subtract $27$ from each side.
$\Rightarrow 3g^2-24g+27-27=0-27$
Simplify.
$\Rightarrow 3g^2-24g=-27$
Divide each side by $3$.
$\Rightarrow \frac{3g^2-24g}{3}=\frac{-27}{3}$
Simplify.
$\Rightarrow g^2-8g=-9$
Find the value of $(\frac{b}{2})^2$.
Substitute $-8$ for $b$.
$=(\frac{-8}{2})^2$
Simplify.
$=(-4)^2$
$=16$
Add $16$ to each side of the equation.
$\Rightarrow g^2-8g+16=-9+16$
Simplify.
$\Rightarrow g^2-8g+16=7$
Write the left side as the square of a binomial.
$\Rightarrow (g-4)^2=7$
Take the square root of each side.
$\Rightarrow g-4=\pm \sqrt{7}$
Add $4$ to each side.
$\Rightarrow g-4+4=\pm \sqrt{7}+4$
Simplify.
$\Rightarrow g=\pm \sqrt{7}+4$
The solutions are $g= \sqrt{7}+4\approx 6.65$ and $g=- \sqrt{7}+4\approx 1.35$.
