x^2+36x+191=0

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Solution for x^2+36x+191=0 equation: 


Simplifying
x2 + 36x + 191 = 0

Reorder the terms:
191 + 36x + x2 = 0

Solving
191 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-191' to each side of the equation.
191 + 36x + -191 + x2 = 0 + -191

Reorder the terms:
191 + -191 + 36x + x2 = 0 + -191

Combine like terms: 191 + -191 = 0
0 + 36x + x2 = 0 + -191
36x + x2 = 0 + -191

Combine like terms: 0 + -191 = -191
36x + x2 = -191

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -191 + 324

Reorder the terms:
324 + 36x + x2 = -191 + 324

Combine like terms: -191 + 324 = 133
324 + 36x + x2 = 133

Factor a perfect square on the left side:
(x + 18)(x + 18) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(x + 18) equal to 11.532562595 and -11.532562595.


Subproblem 1
x + 18 = 11.532562595

Simplifying
x + 18 = 11.532562595

Reorder the terms:
18 + x = 11.532562595

Solving
18 + x = 11.532562595

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 11.532562595 + -18

Combine like terms: 18 + -18 = 0
0 + x = 11.532562595 + -18
x = 11.532562595 + -18

Combine like terms: 11.532562595 + -18 = -6.467437405
x = -6.467437405

Simplifying
x = -6.467437405


Subproblem 2
x + 18 = -11.532562595

Simplifying
x + 18 = -11.532562595

Reorder the terms:
18 + x = -11.532562595

Solving
18 + x = -11.532562595

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -11.532562595 + -18

Combine like terms: 18 + -18 = 0
0 + x = -11.532562595 + -18
x = -11.532562595 + -18

Combine like terms: -11.532562595 + -18 = -29.532562595
x = -29.532562595

Simplifying
x = -29.532562595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.467437405, -29.532562595}

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