(x-10)(x-10)-220=0

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Solution for (x-10)(x-10)-220=0 equation: 


Simplifying
(x + -10)(x + -10) + -220 = 0

Reorder the terms:
(-10 + x)(x + -10) + -220 = 0

Reorder the terms:
(-10 + x)(-10 + x) + -220 = 0

Multiply (-10 + x) * (-10 + x)
(-10(-10 + x) + x(-10 + x)) + -220 = 0
((-10 * -10 + x * -10) + x(-10 + x)) + -220 = 0
((100 + -10x) + x(-10 + x)) + -220 = 0
(100 + -10x + (-10 * x + x * x)) + -220 = 0
(100 + -10x + (-10x + x2)) + -220 = 0

Combine like terms: -10x + -10x = -20x
(100 + -20x + x2) + -220 = 0

Reorder the terms:
100 + -220 + -20x + x2 = 0

Combine like terms: 100 + -220 = -120
-120 + -20x + x2 = 0

Solving
-120 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -20x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -20x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -20x + x2 = 0 + 120
-20x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-20x + x2 = 120

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 = 120 + 100

Reorder the terms:
100 + -20x + x2 = 120 + 100

Combine like terms: 120 + 100 = 220
100 + -20x + x2 = 220

Factor a perfect square on the left side:
(x + -10)(x + -10) = 220

Calculate the square root of the right side: 14.832396974

Break this problem into two subproblems by setting 
(x + -10) equal to 14.832396974 and -14.832396974.


Subproblem 1
x + -10 = 14.832396974

Simplifying
x + -10 = 14.832396974

Reorder the terms:
-10 + x = 14.832396974

Solving
-10 + x = 14.832396974

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = 14.832396974 + 10

Combine like terms: -10 + 10 = 0
0 + x = 14.832396974 + 10
x = 14.832396974 + 10

Combine like terms: 14.832396974 + 10 = 24.832396974
x = 24.832396974

Simplifying
x = 24.832396974


Subproblem 2
x + -10 = -14.832396974

Simplifying
x + -10 = -14.832396974

Reorder the terms:
-10 + x = -14.832396974

Solving
-10 + x = -14.832396974

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = -14.832396974 + 10

Combine like terms: -10 + 10 = 0
0 + x = -14.832396974 + 10
x = -14.832396974 + 10

Combine like terms: -14.832396974 + 10 = -4.832396974
x = -4.832396974

Simplifying
x = -4.832396974


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.832396974, -4.832396974}

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