11x^2-5x-36=0

Solution for 11x^2-5x-36=0 equation:

Simplifying
11x2 + -5x + -36 = 0

Reorder the terms:
-36 + -5x + 11x2 = 0

Solving
-36 + -5x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-3.272727273 + -0.4545454545x + x2 = 0

Move the constant term to the right:

Add '3.272727273' to each side of the equation.
-3.272727273 + -0.4545454545x + 3.272727273 + x2 = 0 + 3.272727273

Reorder the terms:
-3.272727273 + 3.272727273 + -0.4545454545x + x2 = 0 + 3.272727273

Combine like terms: -3.272727273 + 3.272727273 = 0.000000000
0.000000000 + -0.4545454545x + x2 = 0 + 3.272727273
-0.4545454545x + x2 = 0 + 3.272727273

Combine like terms: 0 + 3.272727273 = 3.272727273
-0.4545454545x + x2 = 3.272727273

The x term is -0.4545454545x.  Take half its coefficient (-0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
-0.4545454545x + 0.05165289257 + x2 = 3.272727273 + 0.05165289257

Reorder the terms:
0.05165289257 + -0.4545454545x + x2 = 3.272727273 + 0.05165289257

Combine like terms: 3.272727273 + 0.05165289257 = 3.32438016557
0.05165289257 + -0.4545454545x + x2 = 3.32438016557

Factor a perfect square on the left side:
(x + -0.2272727273)(x + -0.2272727273) = 3.32438016557

Calculate the square root of the right side: 1.823288284

Break this problem into two subproblems by setting 
(x + -0.2272727273) equal to 1.823288284 and -1.823288284.

Subproblem 1
x + -0.2272727273 = 1.823288284

Simplifying
x + -0.2272727273 = 1.823288284

Reorder the terms:
-0.2272727273 + x = 1.823288284

Solving
-0.2272727273 + x = 1.823288284

Solving for variable 'x'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + x = 1.823288284 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + x = 1.823288284 + 0.2272727273
x = 1.823288284 + 0.2272727273

Combine like terms: 1.823288284 + 0.2272727273 = 2.0505610113
x = 2.0505610113

Simplifying
x = 2.0505610113

Subproblem 2
x + -0.2272727273 = -1.823288284

Simplifying
x + -0.2272727273 = -1.823288284

Reorder the terms:
-0.2272727273 + x = -1.823288284

Solving
-0.2272727273 + x = -1.823288284

Solving for variable 'x'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + x = -1.823288284 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + x = -1.823288284 + 0.2272727273
x = -1.823288284 + 0.2272727273

Combine like terms: -1.823288284 + 0.2272727273 = -1.5960155567
x = -1.5960155567

Simplifying
x = -1.5960155567

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0505610113, -1.5960155567}