20x^2-44x-112=0

Solution for 20x^2-44x-112=0 equation:

Simplifying
20x2 + -44x + -112 = 0

Reorder the terms:
-112 + -44x + 20x2 = 0

Solving
-112 + -44x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + -11x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-28 + -11x + 5x2)' equal to zero and attempt to solve:

Simplifying
-28 + -11x + 5x2 = 0

Solving
-28 + -11x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-5.6 + -2.2x + x2 = 0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + -2.2x + 5.6 + x2 = 0 + 5.6

Reorder the terms:
-5.6 + 5.6 + -2.2x + x2 = 0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + -2.2x + x2 = 0 + 5.6
-2.2x + x2 = 0 + 5.6

Combine like terms: 0 + 5.6 = 5.6
-2.2x + x2 = 5.6

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 5.6 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 5.6 + 1.21

Combine like terms: 5.6 + 1.21 = 6.81
1.21 + -2.2x + x2 = 6.81

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 6.81

Calculate the square root of the right side: 2.60959767

Break this problem into two subproblems by setting 
(x + -1.1) equal to 2.60959767 and -2.60959767.

Subproblem 1
x + -1.1 = 2.60959767

Simplifying
x + -1.1 = 2.60959767

Reorder the terms:
-1.1 + x = 2.60959767

Solving
-1.1 + x = 2.60959767

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 2.60959767 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 2.60959767 + 1.1
x = 2.60959767 + 1.1

Combine like terms: 2.60959767 + 1.1 = 3.70959767
x = 3.70959767

Simplifying
x = 3.70959767

Subproblem 2
x + -1.1 = -2.60959767

Simplifying
x + -1.1 = -2.60959767

Reorder the terms:
-1.1 + x = -2.60959767

Solving
-1.1 + x = -2.60959767

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -2.60959767 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -2.60959767 + 1.1
x = -2.60959767 + 1.1

Combine like terms: -2.60959767 + 1.1 = -1.50959767
x = -1.50959767

Simplifying
x = -1.50959767

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.70959767, -1.50959767}
Solution
x = {3.70959767, -1.50959767}