x^2+35.4x-4318.8=0

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Solution for x^2+35.4x-4318.8=0 equation: 


Simplifying
x2 + 35.4x + -4318.8 = 0

Reorder the terms:
-4318.8 + 35.4x + x2 = 0

Solving
-4318.8 + 35.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4318.8' to each side of the equation.
-4318.8 + 35.4x + 4318.8 + x2 = 0 + 4318.8

Reorder the terms:
-4318.8 + 4318.8 + 35.4x + x2 = 0 + 4318.8

Combine like terms: -4318.8 + 4318.8 = 0.0
0.0 + 35.4x + x2 = 0 + 4318.8
35.4x + x2 = 0 + 4318.8

Combine like terms: 0 + 4318.8 = 4318.8
35.4x + x2 = 4318.8

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 = 4318.8 + 313.29

Reorder the terms:
313.29 + 35.4x + x2 = 4318.8 + 313.29

Combine like terms: 4318.8 + 313.29 = 4632.09
313.29 + 35.4x + x2 = 4632.09

Factor a perfect square on the left side:
(x + 17.7)(x + 17.7) = 4632.09

Calculate the square root of the right side: 68.059459298

Break this problem into two subproblems by setting 
(x + 17.7) equal to 68.059459298 and -68.059459298.


Subproblem 1
x + 17.7 = 68.059459298

Simplifying
x + 17.7 = 68.059459298

Reorder the terms:
17.7 + x = 68.059459298

Solving
17.7 + x = 68.059459298

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 = 68.059459298 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = 68.059459298 + -17.7
x = 68.059459298 + -17.7

Combine like terms: 68.059459298 + -17.7 = 50.359459298
x = 50.359459298

Simplifying
x = 50.359459298


Subproblem 2
x + 17.7 = -68.059459298

Simplifying
x + 17.7 = -68.059459298

Reorder the terms:
17.7 + x = -68.059459298

Solving
17.7 + x = -68.059459298

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 = -68.059459298 + -17.7

Combine like terms: 17.7 + -17.7 = 0.0
0.0 + x = -68.059459298 + -17.7
x = -68.059459298 + -17.7

Combine like terms: -68.059459298 + -17.7 = -85.759459298
x = -85.759459298

Simplifying
x = -85.759459298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.359459298, -85.759459298}

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