x^2+5x-156=0

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Solution for x^2+5x-156=0 equation: 


Simplifying
x2 + 5x + -156 = 0

Reorder the terms:
-156 + 5x + x2 = 0

Solving
-156 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + 5x + 156 + x2 = 0 + 156

Reorder the terms:
-156 + 156 + 5x + x2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + 5x + x2 = 0 + 156
5x + x2 = 0 + 156

Combine like terms: 0 + 156 = 156
5x + x2 = 156

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 = 156 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 156 + 6.25

Combine like terms: 156 + 6.25 = 162.25
6.25 + 5x + x2 = 162.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.737739203 and -12.737739203.


Subproblem 1
x + 2.5 = 12.737739203

Simplifying
x + 2.5 = 12.737739203

Reorder the terms:
2.5 + x = 12.737739203

Solving
2.5 + x = 12.737739203

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 = 12.737739203 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.737739203 + -2.5
x = 12.737739203 + -2.5

Combine like terms: 12.737739203 + -2.5 = 10.237739203
x = 10.237739203

Simplifying
x = 10.237739203


Subproblem 2
x + 2.5 = -12.737739203

Simplifying
x + 2.5 = -12.737739203

Reorder the terms:
2.5 + x = -12.737739203

Solving
2.5 + x = -12.737739203

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 = -12.737739203 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.737739203 + -2.5
x = -12.737739203 + -2.5

Combine like terms: -12.737739203 + -2.5 = -15.237739203
x = -15.237739203

Simplifying
x = -15.237739203


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.237739203, -15.237739203}

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