Answer
$w=3.73,-10.73$
Work Step by Step
$w^2+7w-40=0$
or, $w^2+7w=40$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=7$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(7)^2}{4}=\dfrac{49}{4}$
To complete the square, add $\dfrac{49}{4}$ on both sides.
$w^2+7w+\dfrac{49}{4}=40+\dfrac{49}{4}$
$\implies (w+\dfrac{7}{2})^2=\dfrac{209}{4}$
$\implies (w+3.5)^2=52.25$
$\implies (w+3.5)=7.23$
and
$\implies (w+3.5)=-7.23$
or, $w=3.73,-10.73$
