(x+2)(x+2)+4=22

Solution for (x+2)(x+2)+4=22 equation:

(x+2)(x+2)+4=22

We move all terms to the left:

(x+2)(x+2)+4-(22)=0

We add all the numbers together, and all the variables

(x+2)(x+2)-18=0

We multiply parentheses ..

(+x^2+2x+2x+4)-18=0

We get rid of parentheses

x^2+2x+2x+4-18=0

We add all the numbers together, and all the variables

x^2+4x-14=0

a = 1; b = 4; c = -14;
Δ = b2-4ac
Δ = 42-4·1·(-14)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*1}=\frac{-4-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*1}=\frac{-4+6\sqrt{2}}{2}
$