x^2+7x-187=0

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Solution for x^2+7x-187=0 equation: 


Simplifying
x2 + 7x + -187 = 0

Reorder the terms:
-187 + 7x + x2 = 0

Solving
-187 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '187' to each side of the equation.
-187 + 7x + 187 + x2 = 0 + 187

Reorder the terms:
-187 + 187 + 7x + x2 = 0 + 187

Combine like terms: -187 + 187 = 0
0 + 7x + x2 = 0 + 187
7x + x2 = 0 + 187

Combine like terms: 0 + 187 = 187
7x + x2 = 187

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 187 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 187 + 12.25

Combine like terms: 187 + 12.25 = 199.25
12.25 + 7x + x2 = 199.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 199.25

Calculate the square root of the right side: 14.115594213

Break this problem into two subproblems by setting 
(x + 3.5) equal to 14.115594213 and -14.115594213.


Subproblem 1
x + 3.5 = 14.115594213

Simplifying
x + 3.5 = 14.115594213

Reorder the terms:
3.5 + x = 14.115594213

Solving
3.5 + x = 14.115594213

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 14.115594213 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 14.115594213 + -3.5
x = 14.115594213 + -3.5

Combine like terms: 14.115594213 + -3.5 = 10.615594213
x = 10.615594213

Simplifying
x = 10.615594213


Subproblem 2
x + 3.5 = -14.115594213

Simplifying
x + 3.5 = -14.115594213

Reorder the terms:
3.5 + x = -14.115594213

Solving
3.5 + x = -14.115594213

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -14.115594213 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -14.115594213 + -3.5
x = -14.115594213 + -3.5

Combine like terms: -14.115594213 + -3.5 = -17.615594213
x = -17.615594213

Simplifying
x = -17.615594213


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.615594213, -17.615594213}

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