x^2-5x-172=0

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Solution for x^2-5x-172=0 equation: 


Simplifying
x2 + -5x + -172 = 0

Reorder the terms:
-172 + -5x + x2 = 0

Solving
-172 + -5x + 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 + -5x + 172 + x2 = 0 + 172

Reorder the terms:
-172 + 172 + -5x + x2 = 0 + 172

Combine like terms: -172 + 172 = 0
0 + -5x + x2 = 0 + 172
-5x + x2 = 0 + 172

Combine like terms: 0 + 172 = 172
-5x + x2 = 172

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 172 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 172 + 6.25

Combine like terms: 172 + 6.25 = 178.25
6.25 + -5x + x2 = 178.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 178.25

Calculate the square root of the right side: 13.351029923

Break this problem into two subproblems by setting 
(x + -2.5) equal to 13.351029923 and -13.351029923.


Subproblem 1
x + -2.5 = 13.351029923

Simplifying
x + -2.5 = 13.351029923

Reorder the terms:
-2.5 + x = 13.351029923

Solving
-2.5 + x = 13.351029923

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 13.351029923 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 13.351029923 + 2.5
x = 13.351029923 + 2.5

Combine like terms: 13.351029923 + 2.5 = 15.851029923
x = 15.851029923

Simplifying
x = 15.851029923


Subproblem 2
x + -2.5 = -13.351029923

Simplifying
x + -2.5 = -13.351029923

Reorder the terms:
-2.5 + x = -13.351029923

Solving
-2.5 + x = -13.351029923

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -13.351029923 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -13.351029923 + 2.5
x = -13.351029923 + 2.5

Combine like terms: -13.351029923 + 2.5 = -10.851029923
x = -10.851029923

Simplifying
x = -10.851029923


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.851029923, -10.851029923}

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