x^2-20x+8=0

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Solution for x^2-20x+8=0 equation: 


Simplifying
x2 + -20x + 8 = 0

Reorder the terms:
8 + -20x + x2 = 0

Solving
8 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -20x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -20x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -20x + x2 = 0 + -8
-20x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-20x + x2 = -8

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 = -8 + 100

Reorder the terms:
100 + -20x + x2 = -8 + 100

Combine like terms: -8 + 100 = 92
100 + -20x + x2 = 92

Factor a perfect square on the left side:
(x + -10)(x + -10) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + -10) equal to 9.591663047 and -9.591663047.


Subproblem 1
x + -10 = 9.591663047

Simplifying
x + -10 = 9.591663047

Reorder the terms:
-10 + x = 9.591663047

Solving
-10 + x = 9.591663047

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 = 9.591663047 + 10

Combine like terms: -10 + 10 = 0
0 + x = 9.591663047 + 10
x = 9.591663047 + 10

Combine like terms: 9.591663047 + 10 = 19.591663047
x = 19.591663047

Simplifying
x = 19.591663047


Subproblem 2
x + -10 = -9.591663047

Simplifying
x + -10 = -9.591663047

Reorder the terms:
-10 + x = -9.591663047

Solving
-10 + x = -9.591663047

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 = -9.591663047 + 10

Combine like terms: -10 + 10 = 0
0 + x = -9.591663047 + 10
x = -9.591663047 + 10

Combine like terms: -9.591663047 + 10 = 0.408336953
x = 0.408336953

Simplifying
x = 0.408336953


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.591663047, 0.408336953}

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