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

Solution for (x-2)2+(x-2)(x-2)=0 equation:

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

We multiply parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-2x=0

a = 1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*1}=\frac{4}{2}
=2
$