#### Answer

$w=2.14,-5.14$

#### Work Step by Step

$4w^2+12w-44=0$
or, $4w^2+12w=44$
Rewrite the equation as:
$w^2+3w=11$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=3$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(3)^2}{4}=\dfrac{9}{4}$
To complete the square, add $\dfrac{9}{4}$ on both sides.
$w^2+3w+\dfrac{9}{4}=11+\dfrac{9}{4}$
$\implies (w+\dfrac{9}{4})^2=13.25$
$\implies (w+\dfrac{9}{4})=3.64$
and
$\implies (w+\dfrac{9}{4})=-3.64$
or, $w=2.14,-5.14$