x^2+35x+12=0

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Solution for x^2+35x+12=0 equation: 


Simplifying
x2 + 35x + 12 = 0

Reorder the terms:
12 + 35x + x2 = 0

Solving
12 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 35x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 35x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 35x + x2 = 0 + -12
35x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
35x + x2 = -12

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 = -12 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -12 + 306.25

Combine like terms: -12 + 306.25 = 294.25
306.25 + 35x + x2 = 294.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 294.25

Calculate the square root of the right side: 17.153716798

Break this problem into two subproblems by setting 
(x + 17.5) equal to 17.153716798 and -17.153716798.


Subproblem 1
x + 17.5 = 17.153716798

Simplifying
x + 17.5 = 17.153716798

Reorder the terms:
17.5 + x = 17.153716798

Solving
17.5 + x = 17.153716798

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 = 17.153716798 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 17.153716798 + -17.5
x = 17.153716798 + -17.5

Combine like terms: 17.153716798 + -17.5 = -0.346283202
x = -0.346283202

Simplifying
x = -0.346283202


Subproblem 2
x + 17.5 = -17.153716798

Simplifying
x + 17.5 = -17.153716798

Reorder the terms:
17.5 + x = -17.153716798

Solving
17.5 + x = -17.153716798

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 = -17.153716798 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -17.153716798 + -17.5
x = -17.153716798 + -17.5

Combine like terms: -17.153716798 + -17.5 = -34.653716798
x = -34.653716798

Simplifying
x = -34.653716798


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.346283202, -34.653716798}

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