x^2-20x-172=0

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Solution for x^2-20x-172=0 equation: 


Simplifying
x2 + -20x + -172 = 0

Reorder the terms:
-172 + -20x + x2 = 0

Solving
-172 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '172' to each side of the equation.
-172 + -20x + 172 + x2 = 0 + 172

Reorder the terms:
-172 + 172 + -20x + x2 = 0 + 172

Combine like terms: -172 + 172 = 0
0 + -20x + x2 = 0 + 172
-20x + x2 = 0 + 172

Combine like terms: 0 + 172 = 172
-20x + x2 = 172

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 = 172 + 100

Reorder the terms:
100 + -20x + x2 = 172 + 100

Combine like terms: 172 + 100 = 272
100 + -20x + x2 = 272

Factor a perfect square on the left side:
(x + -10)(x + -10) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + -10) equal to 16.492422502 and -16.492422502.


Subproblem 1
x + -10 = 16.492422502

Simplifying
x + -10 = 16.492422502

Reorder the terms:
-10 + x = 16.492422502

Solving
-10 + x = 16.492422502

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 = 16.492422502 + 10

Combine like terms: -10 + 10 = 0
0 + x = 16.492422502 + 10
x = 16.492422502 + 10

Combine like terms: 16.492422502 + 10 = 26.492422502
x = 26.492422502

Simplifying
x = 26.492422502


Subproblem 2
x + -10 = -16.492422502

Simplifying
x + -10 = -16.492422502

Reorder the terms:
-10 + x = -16.492422502

Solving
-10 + x = -16.492422502

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 = -16.492422502 + 10

Combine like terms: -10 + 10 = 0
0 + x = -16.492422502 + 10
x = -16.492422502 + 10

Combine like terms: -16.492422502 + 10 = -6.492422502
x = -6.492422502

Simplifying
x = -6.492422502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.492422502, -6.492422502}

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