x^2-6000x-2880000=0

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Solution for x^2-6000x-2880000=0 equation:


Simplifying
x2 + -6000x + -2880000 = 0

Reorder the terms:
-2880000 + -6000x + x2 = 0

Solving
-2880000 + -6000x + 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 + -6000x + 2880000 + x2 = 0 + 2880000

Reorder the terms:
-2880000 + 2880000 + -6000x + x2 = 0 + 2880000

Combine like terms: -2880000 + 2880000 = 0
0 + -6000x + x2 = 0 + 2880000
-6000x + x2 = 0 + 2880000

Combine like terms: 0 + 2880000 = 2880000
-6000x + x2 = 2880000

The x term is -6000x.  Take half its coefficient (-3000).
Square it (9000000) and add it to both sides.

Add '9000000' to each side of the equation.
-6000x + 9000000 + x2 = 2880000 + 9000000

Reorder the terms:
9000000 + -6000x + x2 = 2880000 + 9000000

Combine like terms: 2880000 + 9000000 = 11880000
9000000 + -6000x + x2 = 11880000

Factor a perfect square on the left side:
(x + -3000)(x + -3000) = 11880000

Calculate the square root of the right side: 3446.737587923

Break this problem into two subproblems by setting 
(x + -3000) equal to 3446.737587923 and -3446.737587923.

Subproblem 1

x + -3000 = 3446.737587923 Simplifying x + -3000 = 3446.737587923 Reorder the terms: -3000 + x = 3446.737587923 Solving -3000 + x = 3446.737587923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + 3000 + x = 3446.737587923 + 3000 Combine like terms: -3000 + 3000 = 0 0 + x = 3446.737587923 + 3000 x = 3446.737587923 + 3000 Combine like terms: 3446.737587923 + 3000 = 6446.737587923 x = 6446.737587923 Simplifying x = 6446.737587923

Subproblem 2

x + -3000 = -3446.737587923 Simplifying x + -3000 = -3446.737587923 Reorder the terms: -3000 + x = -3446.737587923 Solving -3000 + x = -3446.737587923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + 3000 + x = -3446.737587923 + 3000 Combine like terms: -3000 + 3000 = 0 0 + x = -3446.737587923 + 3000 x = -3446.737587923 + 3000 Combine like terms: -3446.737587923 + 3000 = -446.737587923 x = -446.737587923 Simplifying x = -446.737587923

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6446.737587923, -446.737587923}

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