x^2+15x-236=0

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Solution for x^2+15x-236=0 equation: 


Simplifying
x2 + 15x + -236 = 0

Reorder the terms:
-236 + 15x + x2 = 0

Solving
-236 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '236' to each side of the equation.
-236 + 15x + 236 + x2 = 0 + 236

Reorder the terms:
-236 + 236 + 15x + x2 = 0 + 236

Combine like terms: -236 + 236 = 0
0 + 15x + x2 = 0 + 236
15x + x2 = 0 + 236

Combine like terms: 0 + 236 = 236
15x + x2 = 236

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 236 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 236 + 56.25

Combine like terms: 236 + 56.25 = 292.25
56.25 + 15x + x2 = 292.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 292.25

Calculate the square root of the right side: 17.095320997

Break this problem into two subproblems by setting 
(x + 7.5) equal to 17.095320997 and -17.095320997.


Subproblem 1
x + 7.5 = 17.095320997

Simplifying
x + 7.5 = 17.095320997

Reorder the terms:
7.5 + x = 17.095320997

Solving
7.5 + x = 17.095320997

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 17.095320997 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 17.095320997 + -7.5
x = 17.095320997 + -7.5

Combine like terms: 17.095320997 + -7.5 = 9.595320997
x = 9.595320997

Simplifying
x = 9.595320997


Subproblem 2
x + 7.5 = -17.095320997

Simplifying
x + 7.5 = -17.095320997

Reorder the terms:
7.5 + x = -17.095320997

Solving
7.5 + x = -17.095320997

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -17.095320997 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -17.095320997 + -7.5
x = -17.095320997 + -7.5

Combine like terms: -17.095320997 + -7.5 = -24.595320997
x = -24.595320997

Simplifying
x = -24.595320997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.595320997, -24.595320997}

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