x^2+8x-324=0

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Solution for x^2+8x-324=0 equation: 


Simplifying
x2 + 8x + -324 = 0

Reorder the terms:
-324 + 8x + x2 = 0

Solving
-324 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + 8x + 324 + x2 = 0 + 324

Reorder the terms:
-324 + 324 + 8x + x2 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + 8x + x2 = 0 + 324
8x + x2 = 0 + 324

Combine like terms: 0 + 324 = 324
8x + x2 = 324

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 = 324 + 16

Reorder the terms:
16 + 8x + x2 = 324 + 16

Combine like terms: 324 + 16 = 340
16 + 8x + x2 = 340

Factor a perfect square on the left side:
(x + 4)(x + 4) = 340

Calculate the square root of the right side: 18.439088915

Break this problem into two subproblems by setting 
(x + 4) equal to 18.439088915 and -18.439088915.


Subproblem 1
x + 4 = 18.439088915

Simplifying
x + 4 = 18.439088915

Reorder the terms:
4 + x = 18.439088915

Solving
4 + x = 18.439088915

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 = 18.439088915 + -4

Combine like terms: 4 + -4 = 0
0 + x = 18.439088915 + -4
x = 18.439088915 + -4

Combine like terms: 18.439088915 + -4 = 14.439088915
x = 14.439088915

Simplifying
x = 14.439088915


Subproblem 2
x + 4 = -18.439088915

Simplifying
x + 4 = -18.439088915

Reorder the terms:
4 + x = -18.439088915

Solving
4 + x = -18.439088915

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 = -18.439088915 + -4

Combine like terms: 4 + -4 = 0
0 + x = -18.439088915 + -4
x = -18.439088915 + -4

Combine like terms: -18.439088915 + -4 = -22.439088915
x = -22.439088915

Simplifying
x = -22.439088915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.439088915, -22.439088915}

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