x^2+8x-356.5=0

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Solution for x^2+8x-356.5=0 equation: 


Simplifying
x2 + 8x + -356.5 = 0

Reorder the terms:
-356.5 + 8x + x2 = 0

Solving
-356.5 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '356.5' to each side of the equation.
-356.5 + 8x + 356.5 + x2 = 0 + 356.5

Reorder the terms:
-356.5 + 356.5 + 8x + x2 = 0 + 356.5

Combine like terms: -356.5 + 356.5 = 0.0
0.0 + 8x + x2 = 0 + 356.5
8x + x2 = 0 + 356.5

Combine like terms: 0 + 356.5 = 356.5
8x + x2 = 356.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 356.5 + 16

Reorder the terms:
16 + 8x + x2 = 356.5 + 16

Combine like terms: 356.5 + 16 = 372.5
16 + 8x + x2 = 372.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 372.5

Calculate the square root of the right side: 19.300259066

Break this problem into two subproblems by setting 
(x + 4) equal to 19.300259066 and -19.300259066.


Subproblem 1
x + 4 = 19.300259066

Simplifying
x + 4 = 19.300259066

Reorder the terms:
4 + x = 19.300259066

Solving
4 + x = 19.300259066

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 19.300259066 + -4

Combine like terms: 4 + -4 = 0
0 + x = 19.300259066 + -4
x = 19.300259066 + -4

Combine like terms: 19.300259066 + -4 = 15.300259066
x = 15.300259066

Simplifying
x = 15.300259066


Subproblem 2
x + 4 = -19.300259066

Simplifying
x + 4 = -19.300259066

Reorder the terms:
4 + x = -19.300259066

Solving
4 + x = -19.300259066

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -19.300259066 + -4

Combine like terms: 4 + -4 = 0
0 + x = -19.300259066 + -4
x = -19.300259066 + -4

Combine like terms: -19.300259066 + -4 = -23.300259066
x = -23.300259066

Simplifying
x = -23.300259066


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.300259066, -23.300259066}

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