x^2-51957.92x-8330.13=0

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Solution for x^2-51957.92x-8330.13=0 equation:


Simplifying
x2 + -51957.92x + -8330.13 = 0

Reorder the terms:
-8330.13 + -51957.92x + x2 = 0

Solving
-8330.13 + -51957.92x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8330.13' to each side of the equation.
-8330.13 + -51957.92x + 8330.13 + x2 = 0 + 8330.13

Reorder the terms:
-8330.13 + 8330.13 + -51957.92x + x2 = 0 + 8330.13

Combine like terms: -8330.13 + 8330.13 = 0.00
0.00 + -51957.92x + x2 = 0 + 8330.13
-51957.92x + x2 = 0 + 8330.13

Combine like terms: 0 + 8330.13 = 8330.13
-51957.92x + x2 = 8330.13

The x term is -51957.92x.  Take half its coefficient (-25978.96).
Square it (674906362.7) and add it to both sides.

Add '674906362.7' to each side of the equation.
-51957.92x + 674906362.7 + x2 = 8330.13 + 674906362.7

Reorder the terms:
674906362.7 + -51957.92x + x2 = 8330.13 + 674906362.7

Combine like terms: 8330.13 + 674906362.7 = 674914692.83
674906362.7 + -51957.92x + x2 = 674914692.83

Factor a perfect square on the left side:
(x + -25978.96)(x + -25978.96) = 674914692.83

Calculate the square root of the right side: 25979.120324407

Break this problem into two subproblems by setting 
(x + -25978.96) equal to 25979.120324407 and -25979.120324407.


Subproblem 1
x + -25978.96 = 25979.120324407

Simplifying
x + -25978.96 = 25979.120324407

Reorder the terms:
-25978.96 + x = 25979.120324407

Solving
-25978.96 + x = 25979.120324407

Solving for variable 'x'.

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

Add '25978.96' to each side of the equation.
-25978.96 + 25978.96 + x = 25979.120324407 + 25978.96

Combine like terms: -25978.96 + 25978.96 = 0.00
0.00 + x = 25979.120324407 + 25978.96
x = 25979.120324407 + 25978.96

Combine like terms: 25979.120324407 + 25978.96 = 51958.080324407
x = 51958.080324407

Simplifying
x = 51958.080324407


Subproblem 2
x + -25978.96 = -25979.120324407

Simplifying
x + -25978.96 = -25979.120324407

Reorder the terms:
-25978.96 + x = -25979.120324407

Solving
-25978.96 + x = -25979.120324407

Solving for variable 'x'.

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

Add '25978.96' to each side of the equation.
-25978.96 + 25978.96 + x = -25979.120324407 + 25978.96

Combine like terms: -25978.96 + 25978.96 = 0.00
0.00 + x = -25979.120324407 + 25978.96
x = -25979.120324407 + 25978.96

Combine like terms: -25979.120324407 + 25978.96 = -0.160324407
x = -0.160324407

Simplifying
x = -0.160324407


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {51958.080324407, -0.160324407}

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