x^2+225x-12656.25=0

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Solution for x^2+225x-12656.25=0 equation: 


Simplifying
x2 + 225x + -12656.25 = 0

Reorder the terms:
-12656.25 + 225x + x2 = 0

Solving
-12656.25 + 225x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12656.25' to each side of the equation.
-12656.25 + 225x + 12656.25 + x2 = 0 + 12656.25

Reorder the terms:
-12656.25 + 12656.25 + 225x + x2 = 0 + 12656.25

Combine like terms: -12656.25 + 12656.25 = 0.00
0.00 + 225x + x2 = 0 + 12656.25
225x + x2 = 0 + 12656.25

Combine like terms: 0 + 12656.25 = 12656.25
225x + x2 = 12656.25

The x term is 225x.  Take half its coefficient (112.5).
Square it (12656.25) and add it to both sides.

Add '12656.25' to each side of the equation.
225x + 12656.25 + x2 = 12656.25 + 12656.25

Reorder the terms:
12656.25 + 225x + x2 = 12656.25 + 12656.25

Combine like terms: 12656.25 + 12656.25 = 25312.5
12656.25 + 225x + x2 = 25312.5

Factor a perfect square on the left side:
(x + 112.5)(x + 112.5) = 25312.5

Calculate the square root of the right side: 159.099025767

Break this problem into two subproblems by setting 
(x + 112.5) equal to 159.099025767 and -159.099025767.


Subproblem 1
x + 112.5 = 159.099025767

Simplifying
x + 112.5 = 159.099025767

Reorder the terms:
112.5 + x = 159.099025767

Solving
112.5 + x = 159.099025767

Solving for variable 'x'.

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

Add '-112.5' to each side of the equation.
112.5 + -112.5 + x = 159.099025767 + -112.5

Combine like terms: 112.5 + -112.5 = 0.0
0.0 + x = 159.099025767 + -112.5
x = 159.099025767 + -112.5

Combine like terms: 159.099025767 + -112.5 = 46.599025767
x = 46.599025767

Simplifying
x = 46.599025767


Subproblem 2
x + 112.5 = -159.099025767

Simplifying
x + 112.5 = -159.099025767

Reorder the terms:
112.5 + x = -159.099025767

Solving
112.5 + x = -159.099025767

Solving for variable 'x'.

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

Add '-112.5' to each side of the equation.
112.5 + -112.5 + x = -159.099025767 + -112.5

Combine like terms: 112.5 + -112.5 = 0.0
0.0 + x = -159.099025767 + -112.5
x = -159.099025767 + -112.5

Combine like terms: -159.099025767 + -112.5 = -271.599025767
x = -271.599025767

Simplifying
x = -271.599025767


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.599025767, -271.599025767}

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