x^2-1500x+40000=0

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Solution for x^2-1500x+40000=0 equation: 


Simplifying
x2 + -1500x + 40000 = 0

Reorder the terms:
40000 + -1500x + x2 = 0

Solving
40000 + -1500x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40000' to each side of the equation.
40000 + -1500x + -40000 + x2 = 0 + -40000

Reorder the terms:
40000 + -40000 + -1500x + x2 = 0 + -40000

Combine like terms: 40000 + -40000 = 0
0 + -1500x + x2 = 0 + -40000
-1500x + x2 = 0 + -40000

Combine like terms: 0 + -40000 = -40000
-1500x + x2 = -40000

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 = -40000 + 562500

Reorder the terms:
562500 + -1500x + x2 = -40000 + 562500

Combine like terms: -40000 + 562500 = 522500
562500 + -1500x + x2 = 522500

Factor a perfect square on the left side:
(x + -750)(x + -750) = 522500

Calculate the square root of the right side: 722.84161474

Break this problem into two subproblems by setting 
(x + -750) equal to 722.84161474 and -722.84161474.


Subproblem 1
x + -750 = 722.84161474

Simplifying
x + -750 = 722.84161474

Reorder the terms:
-750 + x = 722.84161474

Solving
-750 + x = 722.84161474

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 = 722.84161474 + 750

Combine like terms: -750 + 750 = 0
0 + x = 722.84161474 + 750
x = 722.84161474 + 750

Combine like terms: 722.84161474 + 750 = 1472.84161474
x = 1472.84161474

Simplifying
x = 1472.84161474


Subproblem 2
x + -750 = -722.84161474

Simplifying
x + -750 = -722.84161474

Reorder the terms:
-750 + x = -722.84161474

Solving
-750 + x = -722.84161474

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 = -722.84161474 + 750

Combine like terms: -750 + 750 = 0
0 + x = -722.84161474 + 750
x = -722.84161474 + 750

Combine like terms: -722.84161474 + 750 = 27.15838526
x = 27.15838526

Simplifying
x = 27.15838526


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1472.84161474, 27.15838526}

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