-22=11c(2c+8)

Solution for -22=11c(2c+8) equation:

Simplifying
-22 = 11c(2c + 8)

Reorder the terms:
-22 = 11c(8 + 2c)
-22 = (8 * 11c + 2c * 11c)
-22 = (88c + 22c2)

Solving
-22 = 88c + 22c2

Solving for variable 'c'.

Reorder the terms:
-22 + -88c + -22c2 = 88c + -88c + 22c2 + -22c2

Combine like terms: 88c + -88c = 0
-22 + -88c + -22c2 = 0 + 22c2 + -22c2
-22 + -88c + -22c2 = 22c2 + -22c2

Combine like terms: 22c2 + -22c2 = 0
-22 + -88c + -22c2 = 0

Factor out the Greatest Common Factor (GCF), '-22'.
-22(1 + 4c + c2) = 0

Ignore the factor -22.
Subproblem 1
Set the factor '(1 + 4c + c2)' equal to zero and attempt to solve:

Simplifying
1 + 4c + c2 = 0

Solving
1 + 4c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4c + -1 + c2 = 0 + -1

Reorder the terms:
1 + -1 + 4c + c2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4c + c2 = 0 + -1
4c + c2 = 0 + -1

Combine like terms: 0 + -1 = -1
4c + c2 = -1

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

Add '4' to each side of the equation.
4c + 4 + c2 = -1 + 4

Reorder the terms:
4 + 4c + c2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4c + c2 = 3

Factor a perfect square on the left side:
(c + 2)(c + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(c + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1
c + 2 = 1.732050808

Simplifying
c + 2 = 1.732050808

Reorder the terms:
2 + c = 1.732050808

Solving
2 + c = 1.732050808

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + c = 1.732050808 + -2
c = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
c = -0.267949192

Simplifying
c = -0.267949192

Subproblem 2
c + 2 = -1.732050808

Simplifying
c + 2 = -1.732050808

Reorder the terms:
2 + c = -1.732050808

Solving
2 + c = -1.732050808

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + c = -1.732050808 + -2
c = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
c = -3.732050808

Simplifying
c = -3.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.267949192, -3.732050808}
Solution
c = {-0.267949192, -3.732050808}