x^2+20x-80000=0

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


Simplifying
x2 + 20x + -80000 = 0

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

Solving
-80000 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '80000' to each side of the equation.
-80000 + 20x + 80000 + x2 = 0 + 80000

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

Combine like terms: -80000 + 80000 = 0
0 + 20x + x2 = 0 + 80000
20x + x2 = 0 + 80000

Combine like terms: 0 + 80000 = 80000
20x + x2 = 80000

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 80000 + 100

Reorder the terms:
100 + 20x + x2 = 80000 + 100

Combine like terms: 80000 + 100 = 80100
100 + 20x + x2 = 80100

Factor a perfect square on the left side:
(x + 10)(x + 10) = 80100

Calculate the square root of the right side: 283.019433962

Break this problem into two subproblems by setting 
(x + 10) equal to 283.019433962 and -283.019433962.


Subproblem 1
x + 10 = 283.019433962

Simplifying
x + 10 = 283.019433962

Reorder the terms:
10 + x = 283.019433962

Solving
10 + x = 283.019433962

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 283.019433962 + -10

Combine like terms: 10 + -10 = 0
0 + x = 283.019433962 + -10
x = 283.019433962 + -10

Combine like terms: 283.019433962 + -10 = 273.019433962
x = 273.019433962

Simplifying
x = 273.019433962


Subproblem 2
x + 10 = -283.019433962

Simplifying
x + 10 = -283.019433962

Reorder the terms:
10 + x = -283.019433962

Solving
10 + x = -283.019433962

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -283.019433962 + -10

Combine like terms: 10 + -10 = 0
0 + x = -283.019433962 + -10
x = -283.019433962 + -10

Combine like terms: -283.019433962 + -10 = -293.019433962
x = -293.019433962

Simplifying
x = -293.019433962


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {273.019433962, -293.019433962}

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