4x^2+80x-80=0

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Solution for 4x^2+80x-80=0 equation: 


Simplifying
4x2 + 80x + -80 = 0

Reorder the terms:
-80 + 80x + 4x2 = 0

Solving
-80 + 80x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + 20x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 20x + x2 = 0

Solving
-20 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 20 + 100

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

Combine like terms: 20 + 100 = 120
100 + 20x + x2 = 120

Factor a perfect square on the left side:
(x + 10)(x + 10) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(x + 10) equal to 10.95445115 and -10.95445115.


Subproblem 1
x + 10 = 10.95445115

Simplifying
x + 10 = 10.95445115

Reorder the terms:
10 + x = 10.95445115

Solving
10 + x = 10.95445115

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 = 10.95445115 + -10

Combine like terms: 10 + -10 = 0
0 + x = 10.95445115 + -10
x = 10.95445115 + -10

Combine like terms: 10.95445115 + -10 = 0.95445115
x = 0.95445115

Simplifying
x = 0.95445115


Subproblem 2
x + 10 = -10.95445115

Simplifying
x + 10 = -10.95445115

Reorder the terms:
10 + x = -10.95445115

Solving
10 + x = -10.95445115

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 = -10.95445115 + -10

Combine like terms: 10 + -10 = 0
0 + x = -10.95445115 + -10
x = -10.95445115 + -10

Combine like terms: -10.95445115 + -10 = -20.95445115
x = -20.95445115

Simplifying
x = -20.95445115


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.95445115, -20.95445115}
Solution
x = {0.95445115, -20.95445115}

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