2x^2+22x-80=0

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Solution for 2x^2+22x-80=0 equation: 


Simplifying
2x2 + 22x + -80 = 0

Reorder the terms:
-80 + 22x + 2x2 = 0

Solving
-80 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 11x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + 11x + x2 = 0

Solving
-40 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 11x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 11x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 11x + x2 = 0 + 40
11x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
11x + x2 = 40

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 40 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 40 + 30.25

Combine like terms: 40 + 30.25 = 70.25
30.25 + 11x + x2 = 70.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + 5.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + 5.5 = 8.381527307

Simplifying
x + 5.5 = 8.381527307

Reorder the terms:
5.5 + x = 8.381527307

Solving
5.5 + x = 8.381527307

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 8.381527307 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 8.381527307 + -5.5
x = 8.381527307 + -5.5

Combine like terms: 8.381527307 + -5.5 = 2.881527307
x = 2.881527307

Simplifying
x = 2.881527307


Subproblem 2
x + 5.5 = -8.381527307

Simplifying
x + 5.5 = -8.381527307

Reorder the terms:
5.5 + x = -8.381527307

Solving
5.5 + x = -8.381527307

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -8.381527307 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -8.381527307 + -5.5
x = -8.381527307 + -5.5

Combine like terms: -8.381527307 + -5.5 = -13.881527307
x = -13.881527307

Simplifying
x = -13.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.881527307, -13.881527307}
Solution
x = {2.881527307, -13.881527307}

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