x^2-20x+100=110

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Solution for x^2-20x+100=110 equation: 


Simplifying
x2 + -20x + 100 = 110

Reorder the terms:
100 + -20x + x2 = 110

Solving
100 + -20x + x2 = 110

Solving for variable 'x'.

Reorder the terms:
100 + -110 + -20x + x2 = 110 + -110

Combine like terms: 100 + -110 = -10
-10 + -20x + x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-10 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -20x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -20x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -20x + x2 = 0 + 10
-20x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-20x + x2 = 10

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 = 10 + 100

Reorder the terms:
100 + -20x + x2 = 10 + 100

Combine like terms: 10 + 100 = 110
100 + -20x + x2 = 110

Factor a perfect square on the left side:
(x + -10)(x + -10) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(x + -10) equal to 10.488088482 and -10.488088482.


Subproblem 1
x + -10 = 10.488088482

Simplifying
x + -10 = 10.488088482

Reorder the terms:
-10 + x = 10.488088482

Solving
-10 + x = 10.488088482

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 = 10.488088482 + 10

Combine like terms: -10 + 10 = 0
0 + x = 10.488088482 + 10
x = 10.488088482 + 10

Combine like terms: 10.488088482 + 10 = 20.488088482
x = 20.488088482

Simplifying
x = 20.488088482


Subproblem 2
x + -10 = -10.488088482

Simplifying
x + -10 = -10.488088482

Reorder the terms:
-10 + x = -10.488088482

Solving
-10 + x = -10.488088482

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 = -10.488088482 + 10

Combine like terms: -10 + 10 = 0
0 + x = -10.488088482 + 10
x = -10.488088482 + 10

Combine like terms: -10.488088482 + 10 = -0.488088482
x = -0.488088482

Simplifying
x = -0.488088482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.488088482, -0.488088482}

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