x^2+35.4x-185.124=0

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Solution for x^2+35.4x-185.124=0 equation: 


Simplifying
x2 + 35.4x + -185.124 = 0

Reorder the terms:
-185.124 + 35.4x + x2 = 0

Solving
-185.124 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '185.124' to each side of the equation.
-185.124 + 35.4x + 185.124 + x2 = 0 + 185.124

Reorder the terms:
-185.124 + 185.124 + 35.4x + x2 = 0 + 185.124

Combine like terms: -185.124 + 185.124 = 0.000
0.000 + 35.4x + x2 = 0 + 185.124
35.4x + x2 = 0 + 185.124

Combine like terms: 0 + 185.124 = 185.124
35.4x + x2 = 185.124

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 = 185.124 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 185.124 + 313.29

Combine like terms: 185.124 + 313.29 = 498.414
313.29 + 35.4x + x2 = 498.414

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 498.414

Calculate the square root of the right side: 22.325187569

Break this problem into two subproblems by setting 
(x + 17.7) equal to 22.325187569 and -22.325187569.


Subproblem 1
x + 17.7 = 22.325187569

Simplifying
x + 17.7 = 22.325187569

Reorder the terms:
17.7 + x = 22.325187569

Solving
17.7 + x = 22.325187569

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 = 22.325187569 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 22.325187569 + -17.7
x = 22.325187569 + -17.7

Combine like terms: 22.325187569 + -17.7 = 4.625187569
x = 4.625187569

Simplifying
x = 4.625187569


Subproblem 2
x + 17.7 = -22.325187569

Simplifying
x + 17.7 = -22.325187569

Reorder the terms:
17.7 + x = -22.325187569

Solving
17.7 + x = -22.325187569

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 = -22.325187569 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -22.325187569 + -17.7
x = -22.325187569 + -17.7

Combine like terms: -22.325187569 + -17.7 = -40.025187569
x = -40.025187569

Simplifying
x = -40.025187569


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.625187569, -40.025187569}

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