2x^2-8x-22=0

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Solution for 2x^2-8x-22=0 equation: 


Simplifying
2x2 + -8x + -22 = 0

Reorder the terms:
-22 + -8x + 2x2 = 0

Solving
-22 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-11 + -4x + x2 = 0

Solving
-11 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -4x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x + x2 = 0 + 11
-4x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4x + x2 = 11

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 11 + 4

Reorder the terms:
4 + -4x + x2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4x + x2 = 15

Factor a perfect square on the left side:
(x + -2)(x + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -2) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + -2 = 3.872983346

Simplifying
x + -2 = 3.872983346

Reorder the terms:
-2 + x = 3.872983346

Solving
-2 + x = 3.872983346

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.872983346 + 2
x = 3.872983346 + 2

Combine like terms: 3.872983346 + 2 = 5.872983346
x = 5.872983346

Simplifying
x = 5.872983346


Subproblem 2
x + -2 = -3.872983346

Simplifying
x + -2 = -3.872983346

Reorder the terms:
-2 + x = -3.872983346

Solving
-2 + x = -3.872983346

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.872983346 + 2
x = -3.872983346 + 2

Combine like terms: -3.872983346 + 2 = -1.872983346
x = -1.872983346

Simplifying
x = -1.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.872983346, -1.872983346}
Solution
x = {5.872983346, -1.872983346}

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