x^2+27x-500=0

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Solution for x^2+27x-500=0 equation: 


Simplifying
x2 + 27x + -500 = 0

Reorder the terms:
-500 + 27x + x2 = 0

Solving
-500 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 27x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + 27x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 27x + x2 = 0 + 500
27x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
27x + x2 = 500

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = 500 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 500 + 182.25

Combine like terms: 500 + 182.25 = 682.25
182.25 + 27x + x2 = 682.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 682.25

Calculate the square root of the right side: 26.119915773

Break this problem into two subproblems by setting 
(x + 13.5) equal to 26.119915773 and -26.119915773.


Subproblem 1
x + 13.5 = 26.119915773

Simplifying
x + 13.5 = 26.119915773

Reorder the terms:
13.5 + x = 26.119915773

Solving
13.5 + x = 26.119915773

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 26.119915773 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 26.119915773 + -13.5
x = 26.119915773 + -13.5

Combine like terms: 26.119915773 + -13.5 = 12.619915773
x = 12.619915773

Simplifying
x = 12.619915773


Subproblem 2
x + 13.5 = -26.119915773

Simplifying
x + 13.5 = -26.119915773

Reorder the terms:
13.5 + x = -26.119915773

Solving
13.5 + x = -26.119915773

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -26.119915773 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -26.119915773 + -13.5
x = -26.119915773 + -13.5

Combine like terms: -26.119915773 + -13.5 = -39.619915773
x = -39.619915773

Simplifying
x = -39.619915773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.619915773, -39.619915773}

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