2x^2+22x-154=0

Solution for 2x^2+22x-154=0 equation:

Simplifying
2x2 + 22x + -154 = 0

Reorder the terms:
-154 + 22x + 2x2 = 0

Solving
-154 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-77 + 11x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-77 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-77 + 11x + x2 = 0

Solving
-77 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + 11x + 77 + x2 = 0 + 77

Reorder the terms:
-77 + 77 + 11x + x2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + 11x + x2 = 0 + 77
11x + x2 = 0 + 77

Combine like terms: 0 + 77 = 77
11x + x2 = 77

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 = 77 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 77 + 30.25

Combine like terms: 77 + 30.25 = 107.25
30.25 + 11x + x2 = 107.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 107.25

Calculate the square root of the right side: 10.356157589

Break this problem into two subproblems by setting 
(x + 5.5) equal to 10.356157589 and -10.356157589.

Subproblem 1
x + 5.5 = 10.356157589

Simplifying
x + 5.5 = 10.356157589

Reorder the terms:
5.5 + x = 10.356157589

Solving
5.5 + x = 10.356157589

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 = 10.356157589 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 10.356157589 + -5.5
x = 10.356157589 + -5.5

Combine like terms: 10.356157589 + -5.5 = 4.856157589
x = 4.856157589

Simplifying
x = 4.856157589

Subproblem 2
x + 5.5 = -10.356157589

Simplifying
x + 5.5 = -10.356157589

Reorder the terms:
5.5 + x = -10.356157589

Solving
5.5 + x = -10.356157589

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 = -10.356157589 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -10.356157589 + -5.5
x = -10.356157589 + -5.5

Combine like terms: -10.356157589 + -5.5 = -15.856157589
x = -15.856157589

Simplifying
x = -15.856157589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.856157589, -15.856157589}
Solution
x = {4.856157589, -15.856157589}