x^2+35.4x-656.122=0

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Solution for x^2+35.4x-656.122=0 equation: 


Simplifying
x2 + 35.4x + -656.122 = 0

Reorder the terms:
-656.122 + 35.4x + x2 = 0

Solving
-656.122 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '656.122' to each side of the equation.
-656.122 + 35.4x + 656.122 + x2 = 0 + 656.122

Reorder the terms:
-656.122 + 656.122 + 35.4x + x2 = 0 + 656.122

Combine like terms: -656.122 + 656.122 = 0.000
0.000 + 35.4x + x2 = 0 + 656.122
35.4x + x2 = 0 + 656.122

Combine like terms: 0 + 656.122 = 656.122
35.4x + x2 = 656.122

The x term is 35.4x.  Take half its coefficient (17.7).
Square it (313.29) and add it to both sides.

Add '313.29' to each side of the equation.
35.4x + 313.29 + x2 = 656.122 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 656.122 + 313.29

Combine like terms: 656.122 + 313.29 = 969.412
313.29 + 35.4x + x2 = 969.412

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 969.412

Calculate the square root of the right side: 31.135381803

Break this problem into two subproblems by setting 
(x + 17.7) equal to 31.135381803 and -31.135381803.


Subproblem 1
x + 17.7 = 31.135381803

Simplifying
x + 17.7 = 31.135381803

Reorder the terms:
17.7 + x = 31.135381803

Solving
17.7 + x = 31.135381803

Solving for variable 'x'.

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

Add '-17.7' to each side of the equation.
17.7 + -17.7 + x = 31.135381803 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 31.135381803 + -17.7
x = 31.135381803 + -17.7

Combine like terms: 31.135381803 + -17.7 = 13.435381803
x = 13.435381803

Simplifying
x = 13.435381803


Subproblem 2
x + 17.7 = -31.135381803

Simplifying
x + 17.7 = -31.135381803

Reorder the terms:
17.7 + x = -31.135381803

Solving
17.7 + x = -31.135381803

Solving for variable 'x'.

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

Add '-17.7' to each side of the equation.
17.7 + -17.7 + x = -31.135381803 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -31.135381803 + -17.7
x = -31.135381803 + -17.7

Combine like terms: -31.135381803 + -17.7 = -48.835381803
x = -48.835381803

Simplifying
x = -48.835381803


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.435381803, -48.835381803}

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