(x+11)(x+11)=109

Solution for (x+11)(x+11)=109 equation:

(x+11)(x+11)=109

We move all terms to the left:

(x+11)(x+11)-(109)=0

We multiply parentheses ..

(+x^2+11x+11x+121)-109=0

We get rid of parentheses

x^2+11x+11x+121-109=0

We add all the numbers together, and all the variables

x^2+22x+12=0

a = 1; b = 22; c = +12;
Δ = b2-4ac
Δ = 222-4·1·12
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{109}}{2*1}=\frac{-22-2\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{109}}{2*1}=\frac{-22+2\sqrt{109}}{2}
$