(x-20)(x-20)+x^2=

Solution for (x-20)(x-20)+x^2= equation:

Simplifying
(x + -20)(x + -20) + x2 = 0

Reorder the terms:
(-20 + x)(x + -20) + x2 = 0

Reorder the terms:
(-20 + x)(-20 + x) + x2 = 0

Multiply (-20 + x) * (-20 + x)
(-20(-20 + x) + x(-20 + x)) + x2 = 0
((-20 * -20 + x * -20) + x(-20 + x)) + x2 = 0
((400 + -20x) + x(-20 + x)) + x2 = 0
(400 + -20x + (-20 * x + x * x)) + x2 = 0
(400 + -20x + (-20x + x2)) + x2 = 0

Combine like terms: -20x + -20x = -40x
(400 + -40x + x2) + x2 = 0

Combine like terms: x2 + x2 = 2x2
400 + -40x + 2x2 = 0

Solving
400 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -20x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(200 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
200 + -20x + x2 = 0

Solving
200 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -20x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -20x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -20x + x2 = 0 + -200
-20x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-20x + x2 = -200

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -200 + 100

Reorder the terms:
100 + -20x + x2 = -200 + 100

Combine like terms: -200 + 100 = -100
100 + -20x + x2 = -100

Factor a perfect square on the left side:
(x + -10)(x + -10) = -100

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.