x^2+35x+186=0

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Solution for x^2+35x+186=0 equation: 


Simplifying
x2 + 35x + 186 = 0

Reorder the terms:
186 + 35x + x2 = 0

Solving
186 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-186' to each side of the equation.
186 + 35x + -186 + x2 = 0 + -186

Reorder the terms:
186 + -186 + 35x + x2 = 0 + -186

Combine like terms: 186 + -186 = 0
0 + 35x + x2 = 0 + -186
35x + x2 = 0 + -186

Combine like terms: 0 + -186 = -186
35x + x2 = -186

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -186 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -186 + 306.25

Combine like terms: -186 + 306.25 = 120.25
306.25 + 35x + x2 = 120.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + 17.5) equal to 10.9658561 and -10.9658561.


Subproblem 1
x + 17.5 = 10.9658561

Simplifying
x + 17.5 = 10.9658561

Reorder the terms:
17.5 + x = 10.9658561

Solving
17.5 + x = 10.9658561

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 10.9658561 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 10.9658561 + -17.5
x = 10.9658561 + -17.5

Combine like terms: 10.9658561 + -17.5 = -6.5341439
x = -6.5341439

Simplifying
x = -6.5341439


Subproblem 2
x + 17.5 = -10.9658561

Simplifying
x + 17.5 = -10.9658561

Reorder the terms:
17.5 + x = -10.9658561

Solving
17.5 + x = -10.9658561

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -10.9658561 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -10.9658561 + -17.5
x = -10.9658561 + -17.5

Combine like terms: -10.9658561 + -17.5 = -28.4658561
x = -28.4658561

Simplifying
x = -28.4658561


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.5341439, -28.4658561}

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