x^2+615x-1000=0

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Solution for x^2+615x-1000=0 equation: 


Simplifying
x2 + 615x + -1000 = 0

Reorder the terms:
-1000 + 615x + x2 = 0

Solving
-1000 + 615x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 615x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 615x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 615x + x2 = 0 + 1000
615x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
615x + x2 = 1000

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 = 1000 + 94556.25

Reorder the terms:
94556.25 + 615x + x2 = 1000 + 94556.25

Combine like terms: 1000 + 94556.25 = 95556.25
94556.25 + 615x + x2 = 95556.25

Factor a perfect square on the left side:
(x + 307.5)(x + 307.5) = 95556.25

Calculate the square root of the right side: 309.121739773

Break this problem into two subproblems by setting 
(x + 307.5) equal to 309.121739773 and -309.121739773.


Subproblem 1
x + 307.5 = 309.121739773

Simplifying
x + 307.5 = 309.121739773

Reorder the terms:
307.5 + x = 309.121739773

Solving
307.5 + x = 309.121739773

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 = 309.121739773 + -307.5

Combine like terms: 307.5 + -307.5 = 0.0
0.0 + x = 309.121739773 + -307.5
x = 309.121739773 + -307.5

Combine like terms: 309.121739773 + -307.5 = 1.621739773
x = 1.621739773

Simplifying
x = 1.621739773


Subproblem 2
x + 307.5 = -309.121739773

Simplifying
x + 307.5 = -309.121739773

Reorder the terms:
307.5 + x = -309.121739773

Solving
307.5 + x = -309.121739773

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 = -309.121739773 + -307.5

Combine like terms: 307.5 + -307.5 = 0.0
0.0 + x = -309.121739773 + -307.5
x = -309.121739773 + -307.5

Combine like terms: -309.121739773 + -307.5 = -616.621739773
x = -616.621739773

Simplifying
x = -616.621739773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.621739773, -616.621739773}

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