2x^2-11x-20=0

Solution for 2x^2-11x-20=0 equation:

Simplifying
2x2 + -11x + -20 = 0

Reorder the terms:
-20 + -11x + 2x2 = 0

Solving
-20 + -11x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-10 + -5.5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -5.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -5.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -5.5x + x2 = 0 + 10
-5.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-5.5x + x2 = 10

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 10 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 10 + 7.5625

Combine like terms: 10 + 7.5625 = 17.5625
7.5625 + -5.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.190763654 and -4.190763654.

Subproblem 1
x + -2.75 = 4.190763654

Simplifying
x + -2.75 = 4.190763654

Reorder the terms:
-2.75 + x = 4.190763654

Solving
-2.75 + x = 4.190763654

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.190763654 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.190763654 + 2.75
x = 4.190763654 + 2.75

Combine like terms: 4.190763654 + 2.75 = 6.940763654
x = 6.940763654

Simplifying
x = 6.940763654

Subproblem 2
x + -2.75 = -4.190763654

Simplifying
x + -2.75 = -4.190763654

Reorder the terms:
-2.75 + x = -4.190763654

Solving
-2.75 + x = -4.190763654

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.190763654 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.190763654 + 2.75
x = -4.190763654 + 2.75

Combine like terms: -4.190763654 + 2.75 = -1.440763654
x = -1.440763654

Simplifying
x = -1.440763654

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.940763654, -1.440763654}