x^2-5x-9560=0

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Solution for x^2-5x-9560=0 equation: 


Simplifying
x2 + -5x + -9560 = 0

Reorder the terms:
-9560 + -5x + x2 = 0

Solving
-9560 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9560' to each side of the equation.
-9560 + -5x + 9560 + x2 = 0 + 9560

Reorder the terms:
-9560 + 9560 + -5x + x2 = 0 + 9560

Combine like terms: -9560 + 9560 = 0
0 + -5x + x2 = 0 + 9560
-5x + x2 = 0 + 9560

Combine like terms: 0 + 9560 = 9560
-5x + x2 = 9560

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 9560 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 9560 + 6.25

Combine like terms: 9560 + 6.25 = 9566.25
6.25 + -5x + x2 = 9566.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9566.25

Calculate the square root of the right side: 97.807208323

Break this problem into two subproblems by setting 
(x + -2.5) equal to 97.807208323 and -97.807208323.


Subproblem 1
x + -2.5 = 97.807208323

Simplifying
x + -2.5 = 97.807208323

Reorder the terms:
-2.5 + x = 97.807208323

Solving
-2.5 + x = 97.807208323

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 97.807208323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 97.807208323 + 2.5
x = 97.807208323 + 2.5

Combine like terms: 97.807208323 + 2.5 = 100.307208323
x = 100.307208323

Simplifying
x = 100.307208323


Subproblem 2
x + -2.5 = -97.807208323

Simplifying
x + -2.5 = -97.807208323

Reorder the terms:
-2.5 + x = -97.807208323

Solving
-2.5 + x = -97.807208323

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -97.807208323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -97.807208323 + 2.5
x = -97.807208323 + 2.5

Combine like terms: -97.807208323 + 2.5 = -95.307208323
x = -95.307208323

Simplifying
x = -95.307208323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {100.307208323, -95.307208323}

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