x^2+545x-7500=0

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Solution for x^2+545x-7500=0 equation: 


Simplifying
x2 + 545x + -7500 = 0

Reorder the terms:
-7500 + 545x + x2 = 0

Solving
-7500 + 545x + 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 + 545x + 7500 + x2 = 0 + 7500

Reorder the terms:
-7500 + 7500 + 545x + x2 = 0 + 7500

Combine like terms: -7500 + 7500 = 0
0 + 545x + x2 = 0 + 7500
545x + x2 = 0 + 7500

Combine like terms: 0 + 7500 = 7500
545x + x2 = 7500

The x term is 545x.  Take half its coefficient (272.5).
Square it (74256.25) and add it to both sides.

Add '74256.25' to each side of the equation.
545x + 74256.25 + x2 = 7500 + 74256.25

Reorder the terms:
74256.25 + 545x + x2 = 7500 + 74256.25

Combine like terms: 7500 + 74256.25 = 81756.25
74256.25 + 545x + x2 = 81756.25

Factor a perfect square on the left side:
(x + 272.5)(x + 272.5) = 81756.25

Calculate the square root of the right side: 285.930498548

Break this problem into two subproblems by setting 
(x + 272.5) equal to 285.930498548 and -285.930498548.


Subproblem 1
x + 272.5 = 285.930498548

Simplifying
x + 272.5 = 285.930498548

Reorder the terms:
272.5 + x = 285.930498548

Solving
272.5 + x = 285.930498548

Solving for variable 'x'.

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

Add '-272.5' to each side of the equation.
272.5 + -272.5 + x = 285.930498548 + -272.5

Combine like terms: 272.5 + -272.5 = 0.0
0.0 + x = 285.930498548 + -272.5
x = 285.930498548 + -272.5

Combine like terms: 285.930498548 + -272.5 = 13.430498548
x = 13.430498548

Simplifying
x = 13.430498548


Subproblem 2
x + 272.5 = -285.930498548

Simplifying
x + 272.5 = -285.930498548

Reorder the terms:
272.5 + x = -285.930498548

Solving
272.5 + x = -285.930498548

Solving for variable 'x'.

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

Add '-272.5' to each side of the equation.
272.5 + -272.5 + x = -285.930498548 + -272.5

Combine like terms: 272.5 + -272.5 = 0.0
0.0 + x = -285.930498548 + -272.5
x = -285.930498548 + -272.5

Combine like terms: -285.930498548 + -272.5 = -558.430498548
x = -558.430498548

Simplifying
x = -558.430498548


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.430498548, -558.430498548}

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