-10x^2-11x-2=0

Solution for -10x^2-11x-2=0 equation:

Simplifying
-10x2 + -11x + -2 = 0

Reorder the terms:
-2 + -11x + -10x2 = 0

Solving
-2 + -11x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 11x + 10x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 11x + 10x2)' equal to zero and attempt to solve:

Simplifying
2 + 11x + 10x2 = 0

Solving
2 + 11x + 10x2 = 0

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

Divide each side by '10'.
0.2 + 1.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.1x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.1x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.1x + x2 = 0.0 + -0.2
1.1x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
1.1x + x2 = -0.2

The x term is 1.1x.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1x + 0.3025 + x2 = -0.2 + 0.3025

Reorder the terms:
0.3025 + 1.1x + x2 = -0.2 + 0.3025

Combine like terms: -0.2 + 0.3025 = 0.1025
0.3025 + 1.1x + x2 = 0.1025

Factor a perfect square on the left side:
(x + 0.55)(x + 0.55) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(x + 0.55) equal to 0.320156212 and -0.320156212.

Subproblem 1
x + 0.55 = 0.320156212

Simplifying
x + 0.55 = 0.320156212

Reorder the terms:
0.55 + x = 0.320156212

Solving
0.55 + x = 0.320156212

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = 0.320156212 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = 0.320156212 + -0.55
x = 0.320156212 + -0.55

Combine like terms: 0.320156212 + -0.55 = -0.229843788
x = -0.229843788

Simplifying
x = -0.229843788

Subproblem 2
x + 0.55 = -0.320156212

Simplifying
x + 0.55 = -0.320156212

Reorder the terms:
0.55 + x = -0.320156212

Solving
0.55 + x = -0.320156212

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = -0.320156212 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = -0.320156212 + -0.55
x = -0.320156212 + -0.55

Combine like terms: -0.320156212 + -0.55 = -0.870156212
x = -0.870156212

Simplifying
x = -0.870156212

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.229843788, -0.870156212}
Solution
x = {-0.229843788, -0.870156212}