x^2+8000x-517744000=0

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Solution for x^2+8000x-517744000=0 equation:


Simplifying
x2 + 8000x + -517744000 = 0

Reorder the terms:
-517744000 + 8000x + x2 = 0

Solving
-517744000 + 8000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '517744000' to each side of the equation.
-517744000 + 8000x + 517744000 + x2 = 0 + 517744000

Reorder the terms:
-517744000 + 517744000 + 8000x + x2 = 0 + 517744000

Combine like terms: -517744000 + 517744000 = 0
0 + 8000x + x2 = 0 + 517744000
8000x + x2 = 0 + 517744000

Combine like terms: 0 + 517744000 = 517744000
8000x + x2 = 517744000

The x term is 8000x.  Take half its coefficient (4000).
Square it (16000000) and add it to both sides.

Add '16000000' to each side of the equation.
8000x + 16000000 + x2 = 517744000 + 16000000

Reorder the terms:
16000000 + 8000x + x2 = 517744000 + 16000000

Combine like terms: 517744000 + 16000000 = 533744000
16000000 + 8000x + x2 = 533744000

Factor a perfect square on the left side:
(x + 4000)(x + 4000) = 533744000

Calculate the square root of the right side: 23102.900250834

Break this problem into two subproblems by setting 
(x + 4000) equal to 23102.900250834 and -23102.900250834.

Subproblem 1

x + 4000 = 23102.900250834 Simplifying x + 4000 = 23102.900250834 Reorder the terms: 4000 + x = 23102.900250834 Solving 4000 + x = 23102.900250834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000' to each side of the equation. 4000 + -4000 + x = 23102.900250834 + -4000 Combine like terms: 4000 + -4000 = 0 0 + x = 23102.900250834 + -4000 x = 23102.900250834 + -4000 Combine like terms: 23102.900250834 + -4000 = 19102.900250834 x = 19102.900250834 Simplifying x = 19102.900250834

Subproblem 2

x + 4000 = -23102.900250834 Simplifying x + 4000 = -23102.900250834 Reorder the terms: 4000 + x = -23102.900250834 Solving 4000 + x = -23102.900250834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000' to each side of the equation. 4000 + -4000 + x = -23102.900250834 + -4000 Combine like terms: 4000 + -4000 = 0 0 + x = -23102.900250834 + -4000 x = -23102.900250834 + -4000 Combine like terms: -23102.900250834 + -4000 = -27102.900250834 x = -27102.900250834 Simplifying x = -27102.900250834

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19102.900250834, -27102.900250834}

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