-x^2+1500x+360=0

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Solution for -x^2+1500x+360=0 equation: 


Simplifying
-1x2 + 1500x + 360 = 0

Reorder the terms:
360 + 1500x + -1x2 = 0

Solving
360 + 1500x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-360 + -1500x + x2 = 0

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + -1500x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + -1500x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + -1500x + x2 = 0 + 360
-1500x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
-1500x + x2 = 360

The x term is -1500x.  Take half its coefficient (-750).
Square it (562500) and add it to both sides.

Add '562500' to each side of the equation.
-1500x + 562500 + x2 = 360 + 562500

Reorder the terms:
562500 + -1500x + x2 = 360 + 562500

Combine like terms: 360 + 562500 = 562860
562500 + -1500x + x2 = 562860

Factor a perfect square on the left side:
(x + -750)(x + -750) = 562860

Calculate the square root of the right side: 750.239961612

Break this problem into two subproblems by setting 
(x + -750) equal to 750.239961612 and -750.239961612.


Subproblem 1
x + -750 = 750.239961612

Simplifying
x + -750 = 750.239961612

Reorder the terms:
-750 + x = 750.239961612

Solving
-750 + x = 750.239961612

Solving for variable 'x'.

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

Add '750' to each side of the equation.
-750 + 750 + x = 750.239961612 + 750

Combine like terms: -750 + 750 = 0
0 + x = 750.239961612 + 750
x = 750.239961612 + 750

Combine like terms: 750.239961612 + 750 = 1500.239961612
x = 1500.239961612

Simplifying
x = 1500.239961612


Subproblem 2
x + -750 = -750.239961612

Simplifying
x + -750 = -750.239961612

Reorder the terms:
-750 + x = -750.239961612

Solving
-750 + x = -750.239961612

Solving for variable 'x'.

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

Add '750' to each side of the equation.
-750 + 750 + x = -750.239961612 + 750

Combine like terms: -750 + 750 = 0
0 + x = -750.239961612 + 750
x = -750.239961612 + 750

Combine like terms: -750.239961612 + 750 = -0.239961612
x = -0.239961612

Simplifying
x = -0.239961612


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1500.239961612, -0.239961612}

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