x^2+5x-137=0

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Solution for x^2+5x-137=0 equation: 


Simplifying
x2 + 5x + -137 = 0

Reorder the terms:
-137 + 5x + x2 = 0

Solving
-137 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '137' to each side of the equation.
-137 + 5x + 137 + x2 = 0 + 137

Reorder the terms:
-137 + 137 + 5x + x2 = 0 + 137

Combine like terms: -137 + 137 = 0
0 + 5x + x2 = 0 + 137
5x + x2 = 0 + 137

Combine like terms: 0 + 137 = 137
5x + x2 = 137

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 = 137 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 137 + 6.25

Combine like terms: 137 + 6.25 = 143.25
6.25 + 5x + x2 = 143.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 143.25

Calculate the square root of the right side: 11.968709204

Break this problem into two subproblems by setting 
(x + 2.5) equal to 11.968709204 and -11.968709204.


Subproblem 1
x + 2.5 = 11.968709204

Simplifying
x + 2.5 = 11.968709204

Reorder the terms:
2.5 + x = 11.968709204

Solving
2.5 + x = 11.968709204

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 = 11.968709204 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 11.968709204 + -2.5
x = 11.968709204 + -2.5

Combine like terms: 11.968709204 + -2.5 = 9.468709204
x = 9.468709204

Simplifying
x = 9.468709204


Subproblem 2
x + 2.5 = -11.968709204

Simplifying
x + 2.5 = -11.968709204

Reorder the terms:
2.5 + x = -11.968709204

Solving
2.5 + x = -11.968709204

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 = -11.968709204 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -11.968709204 + -2.5
x = -11.968709204 + -2.5

Combine like terms: -11.968709204 + -2.5 = -14.468709204
x = -14.468709204

Simplifying
x = -14.468709204


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.468709204, -14.468709204}

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