x^2+615x-36000=0

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Solution for x^2+615x-36000=0 equation: 


Simplifying
x2 + 615x + -36000 = 0

Reorder the terms:
-36000 + 615x + x2 = 0

Solving
-36000 + 615x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36000' to each side of the equation.
-36000 + 615x + 36000 + x2 = 0 + 36000

Reorder the terms:
-36000 + 36000 + 615x + x2 = 0 + 36000

Combine like terms: -36000 + 36000 = 0
0 + 615x + x2 = 0 + 36000
615x + x2 = 0 + 36000

Combine like terms: 0 + 36000 = 36000
615x + x2 = 36000

The x term is 615x.  Take half its coefficient (307.5).
Square it (94556.25) and add it to both sides.

Add '94556.25' to each side of the equation.
615x + 94556.25 + x2 = 36000 + 94556.25

Reorder the terms:
94556.25 + 615x + x2 = 36000 + 94556.25

Combine like terms: 36000 + 94556.25 = 130556.25
94556.25 + 615x + x2 = 130556.25

Factor a perfect square on the left side:
(x + 307.5)(x + 307.5) = 130556.25

Calculate the square root of the right side: 361.325684113

Break this problem into two subproblems by setting 
(x + 307.5) equal to 361.325684113 and -361.325684113.


Subproblem 1
x + 307.5 = 361.325684113

Simplifying
x + 307.5 = 361.325684113

Reorder the terms:
307.5 + x = 361.325684113

Solving
307.5 + x = 361.325684113

Solving for variable 'x'.

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

Add '-307.5' to each side of the equation.
307.5 + -307.5 + x = 361.325684113 + -307.5

Combine like terms: 307.5 + -307.5 = 0.0
0.0 + x = 361.325684113 + -307.5
x = 361.325684113 + -307.5

Combine like terms: 361.325684113 + -307.5 = 53.825684113
x = 53.825684113

Simplifying
x = 53.825684113


Subproblem 2
x + 307.5 = -361.325684113

Simplifying
x + 307.5 = -361.325684113

Reorder the terms:
307.5 + x = -361.325684113

Solving
307.5 + x = -361.325684113

Solving for variable 'x'.

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

Add '-307.5' to each side of the equation.
307.5 + -307.5 + x = -361.325684113 + -307.5

Combine like terms: 307.5 + -307.5 = 0.0
0.0 + x = -361.325684113 + -307.5
x = -361.325684113 + -307.5

Combine like terms: -361.325684113 + -307.5 = -668.825684113
x = -668.825684113

Simplifying
x = -668.825684113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.825684113, -668.825684113}

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