x^2+515x-7500=0

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Solution for x^2+515x-7500=0 equation: 


Simplifying
x2 + 515x + -7500 = 0

Reorder the terms:
-7500 + 515x + x2 = 0

Solving
-7500 + 515x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7500' to each side of the equation.
-7500 + 515x + 7500 + x2 = 0 + 7500

Reorder the terms:
-7500 + 7500 + 515x + x2 = 0 + 7500

Combine like terms: -7500 + 7500 = 0
0 + 515x + x2 = 0 + 7500
515x + x2 = 0 + 7500

Combine like terms: 0 + 7500 = 7500
515x + x2 = 7500

The x term is 515x.  Take half its coefficient (257.5).
Square it (66306.25) and add it to both sides.

Add '66306.25' to each side of the equation.
515x + 66306.25 + x2 = 7500 + 66306.25

Reorder the terms:
66306.25 + 515x + x2 = 7500 + 66306.25

Combine like terms: 7500 + 66306.25 = 73806.25
66306.25 + 515x + x2 = 73806.25

Factor a perfect square on the left side:
(x + 257.5)(x + 257.5) = 73806.25

Calculate the square root of the right side: 271.673057185

Break this problem into two subproblems by setting 
(x + 257.5) equal to 271.673057185 and -271.673057185.


Subproblem 1
x + 257.5 = 271.673057185

Simplifying
x + 257.5 = 271.673057185

Reorder the terms:
257.5 + x = 271.673057185

Solving
257.5 + x = 271.673057185

Solving for variable 'x'.

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

Add '-257.5' to each side of the equation.
257.5 + -257.5 + x = 271.673057185 + -257.5

Combine like terms: 257.5 + -257.5 = 0.0
0.0 + x = 271.673057185 + -257.5
x = 271.673057185 + -257.5

Combine like terms: 271.673057185 + -257.5 = 14.173057185
x = 14.173057185

Simplifying
x = 14.173057185


Subproblem 2
x + 257.5 = -271.673057185

Simplifying
x + 257.5 = -271.673057185

Reorder the terms:
257.5 + x = -271.673057185

Solving
257.5 + x = -271.673057185

Solving for variable 'x'.

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

Add '-257.5' to each side of the equation.
257.5 + -257.5 + x = -271.673057185 + -257.5

Combine like terms: 257.5 + -257.5 = 0.0
0.0 + x = -271.673057185 + -257.5
x = -271.673057185 + -257.5

Combine like terms: -271.673057185 + -257.5 = -529.173057185
x = -529.173057185

Simplifying
x = -529.173057185


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.173057185, -529.173057185}

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