x^2-600x-2880000=0

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Solution for x^2-600x-2880000=0 equation:


Simplifying
x2 + -600x + -2880000 = 0

Reorder the terms:
-2880000 + -600x + x2 = 0

Solving
-2880000 + -600x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2880000' to each side of the equation.
-2880000 + -600x + 2880000 + x2 = 0 + 2880000

Reorder the terms:
-2880000 + 2880000 + -600x + x2 = 0 + 2880000

Combine like terms: -2880000 + 2880000 = 0
0 + -600x + x2 = 0 + 2880000
-600x + x2 = 0 + 2880000

Combine like terms: 0 + 2880000 = 2880000
-600x + x2 = 2880000

The x term is -600x.  Take half its coefficient (-300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
-600x + 90000 + x2 = 2880000 + 90000

Reorder the terms:
90000 + -600x + x2 = 2880000 + 90000

Combine like terms: 2880000 + 90000 = 2970000
90000 + -600x + x2 = 2970000

Factor a perfect square on the left side:
(x + -300)(x + -300) = 2970000

Calculate the square root of the right side: 1723.368793961

Break this problem into two subproblems by setting 
(x + -300) equal to 1723.368793961 and -1723.368793961.

Subproblem 1

x + -300 = 1723.368793961 Simplifying x + -300 = 1723.368793961 Reorder the terms: -300 + x = 1723.368793961 Solving -300 + x = 1723.368793961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 1723.368793961 + 300 Combine like terms: -300 + 300 = 0 0 + x = 1723.368793961 + 300 x = 1723.368793961 + 300 Combine like terms: 1723.368793961 + 300 = 2023.368793961 x = 2023.368793961 Simplifying x = 2023.368793961

Subproblem 2

x + -300 = -1723.368793961 Simplifying x + -300 = -1723.368793961 Reorder the terms: -300 + x = -1723.368793961 Solving -300 + x = -1723.368793961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -1723.368793961 + 300 Combine like terms: -300 + 300 = 0 0 + x = -1723.368793961 + 300 x = -1723.368793961 + 300 Combine like terms: -1723.368793961 + 300 = -1423.368793961 x = -1423.368793961 Simplifying x = -1423.368793961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2023.368793961, -1423.368793961}

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