(w+4)(w+4)-44=0

Solution for (w+4)(w+4)-44=0 equation:

(w+4)(w+4)-44=0

We multiply parentheses ..

(+w^2+4w+4w+16)-44=0

We get rid of parentheses

w^2+4w+4w+16-44=0

We add all the numbers together, and all the variables

w^2+8w-28=0

a = 1; b = 8; c = -28;
Δ = b2-4ac
Δ = 82-4·1·(-28)
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{11}}{2*1}=\frac{-8-4\sqrt{11}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{11}}{2*1}=\frac{-8+4\sqrt{11}}{2}
$