(x-2)(x-2)+16=66

Solution for (x-2)(x-2)+16=66 equation:

(x-2)(x-2)+16=66

We move all terms to the left:

(x-2)(x-2)+16-(66)=0

We add all the numbers together, and all the variables

(x-2)(x-2)-50=0

We multiply parentheses ..

(+x^2-2x-2x+4)-50=0

We get rid of parentheses

x^2-2x-2x+4-50=0

We add all the numbers together, and all the variables

x^2-4x-46=0

a = 1; b = -4; c = -46;
Δ = b2-4ac
Δ = -42-4·1·(-46)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10\sqrt{2}}{2*1}=\frac{4-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10\sqrt{2}}{2*1}=\frac{4+10\sqrt{2}}{2}
$