x^2+5x-10000=0

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Solution for x^2+5x-10000=0 equation: 


Simplifying
x2 + 5x + -10000 = 0

Reorder the terms:
-10000 + 5x + x2 = 0

Solving
-10000 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + 5x + 10000 + x2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + 5x + x2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + 5x + x2 = 0 + 10000
5x + x2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
5x + x2 = 10000

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 = 10000 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 10000 + 6.25

Combine like terms: 10000 + 6.25 = 10006.25
6.25 + 5x + x2 = 10006.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 10006.25

Calculate the square root of the right side: 100.031245119

Break this problem into two subproblems by setting 
(x + 2.5) equal to 100.031245119 and -100.031245119.


Subproblem 1
x + 2.5 = 100.031245119

Simplifying
x + 2.5 = 100.031245119

Reorder the terms:
2.5 + x = 100.031245119

Solving
2.5 + x = 100.031245119

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 = 100.031245119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 100.031245119 + -2.5
x = 100.031245119 + -2.5

Combine like terms: 100.031245119 + -2.5 = 97.531245119
x = 97.531245119

Simplifying
x = 97.531245119


Subproblem 2
x + 2.5 = -100.031245119

Simplifying
x + 2.5 = -100.031245119

Reorder the terms:
2.5 + x = -100.031245119

Solving
2.5 + x = -100.031245119

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 = -100.031245119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -100.031245119 + -2.5
x = -100.031245119 + -2.5

Combine like terms: -100.031245119 + -2.5 = -102.531245119
x = -102.531245119

Simplifying
x = -102.531245119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {97.531245119, -102.531245119}

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