x^2+35.4x-511.52=0

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Solution for x^2+35.4x-511.52=0 equation: 


Simplifying
x2 + 35.4x + -511.52 = 0

Reorder the terms:
-511.52 + 35.4x + x2 = 0

Solving
-511.52 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '511.52' to each side of the equation.
-511.52 + 35.4x + 511.52 + x2 = 0 + 511.52

Reorder the terms:
-511.52 + 511.52 + 35.4x + x2 = 0 + 511.52

Combine like terms: -511.52 + 511.52 = 0.00
0.00 + 35.4x + x2 = 0 + 511.52
35.4x + x2 = 0 + 511.52

Combine like terms: 0 + 511.52 = 511.52
35.4x + x2 = 511.52

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 = 511.52 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 511.52 + 313.29

Combine like terms: 511.52 + 313.29 = 824.81
313.29 + 35.4x + x2 = 824.81

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 824.81

Calculate the square root of the right side: 28.719505567

Break this problem into two subproblems by setting 
(x + 17.7) equal to 28.719505567 and -28.719505567.


Subproblem 1
x + 17.7 = 28.719505567

Simplifying
x + 17.7 = 28.719505567

Reorder the terms:
17.7 + x = 28.719505567

Solving
17.7 + x = 28.719505567

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 = 28.719505567 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 28.719505567 + -17.7
x = 28.719505567 + -17.7

Combine like terms: 28.719505567 + -17.7 = 11.019505567
x = 11.019505567

Simplifying
x = 11.019505567


Subproblem 2
x + 17.7 = -28.719505567

Simplifying
x + 17.7 = -28.719505567

Reorder the terms:
17.7 + x = -28.719505567

Solving
17.7 + x = -28.719505567

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 = -28.719505567 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -28.719505567 + -17.7
x = -28.719505567 + -17.7

Combine like terms: -28.719505567 + -17.7 = -46.419505567
x = -46.419505567

Simplifying
x = -46.419505567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.019505567, -46.419505567}

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