2x^2-80x-80=0

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Solution for 2x^2-80x-80=0 equation: 


Simplifying
2x2 + -80x + -80 = 0

Reorder the terms:
-80 + -80x + 2x2 = 0

Solving
-80 + -80x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -40x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + -40x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + -40x + x2 = 0

Solving
-40 + -40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -40x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -40x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -40x + x2 = 0 + 40
-40x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-40x + x2 = 40

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 40 + 400

Reorder the terms:
400 + -40x + x2 = 40 + 400

Combine like terms: 40 + 400 = 440
400 + -40x + x2 = 440

Factor a perfect square on the left side:
(x + -20)(x + -20) = 440

Calculate the square root of the right side: 20.976176963

Break this problem into two subproblems by setting 
(x + -20) equal to 20.976176963 and -20.976176963.


Subproblem 1
x + -20 = 20.976176963

Simplifying
x + -20 = 20.976176963

Reorder the terms:
-20 + x = 20.976176963

Solving
-20 + x = 20.976176963

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 20.976176963 + 20

Combine like terms: -20 + 20 = 0
0 + x = 20.976176963 + 20
x = 20.976176963 + 20

Combine like terms: 20.976176963 + 20 = 40.976176963
x = 40.976176963

Simplifying
x = 40.976176963


Subproblem 2
x + -20 = -20.976176963

Simplifying
x + -20 = -20.976176963

Reorder the terms:
-20 + x = -20.976176963

Solving
-20 + x = -20.976176963

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -20.976176963 + 20

Combine like terms: -20 + 20 = 0
0 + x = -20.976176963 + 20
x = -20.976176963 + 20

Combine like terms: -20.976176963 + 20 = -0.976176963
x = -0.976176963

Simplifying
x = -0.976176963


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.976176963, -0.976176963}
Solution
x = {40.976176963, -0.976176963}

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