2x^2+20x-80000=0

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Solution for 2x^2+20x-80000=0 equation: 


Simplifying
2x2 + 20x + -80000 = 0

Reorder the terms:
-80000 + 20x + 2x2 = 0

Solving
-80000 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40000 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40000 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-40000 + 10x + x2 = 0

Solving
-40000 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40000' to each side of the equation.
-40000 + 10x + 40000 + x2 = 0 + 40000

Reorder the terms:
-40000 + 40000 + 10x + x2 = 0 + 40000

Combine like terms: -40000 + 40000 = 0
0 + 10x + x2 = 0 + 40000
10x + x2 = 0 + 40000

Combine like terms: 0 + 40000 = 40000
10x + x2 = 40000

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 40000 + 25

Reorder the terms:
25 + 10x + x2 = 40000 + 25

Combine like terms: 40000 + 25 = 40025
25 + 10x + x2 = 40025

Factor a perfect square on the left side:
(x + 5)(x + 5) = 40025

Calculate the square root of the right side: 200.062490237

Break this problem into two subproblems by setting 
(x + 5) equal to 200.062490237 and -200.062490237.


Subproblem 1
x + 5 = 200.062490237

Simplifying
x + 5 = 200.062490237

Reorder the terms:
5 + x = 200.062490237

Solving
5 + x = 200.062490237

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 200.062490237 + -5

Combine like terms: 5 + -5 = 0
0 + x = 200.062490237 + -5
x = 200.062490237 + -5

Combine like terms: 200.062490237 + -5 = 195.062490237
x = 195.062490237

Simplifying
x = 195.062490237


Subproblem 2
x + 5 = -200.062490237

Simplifying
x + 5 = -200.062490237

Reorder the terms:
5 + x = -200.062490237

Solving
5 + x = -200.062490237

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -200.062490237 + -5

Combine like terms: 5 + -5 = 0
0 + x = -200.062490237 + -5
x = -200.062490237 + -5

Combine like terms: -200.062490237 + -5 = -205.062490237
x = -205.062490237

Simplifying
x = -205.062490237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {195.062490237, -205.062490237}
Solution
x = {195.062490237, -205.062490237}

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