2x^2-8x-10x=-10

Solution for 2x^2-8x-10x=-10 equation:

Simplifying
2x2 + -8x + -10x = -10

Reorder the terms:
-8x + -10x + 2x2 = -10

Combine like terms: -8x + -10x = -18x
-18x + 2x2 = -10

Solving
-18x + 2x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + -18x + 2x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -9x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -9x + x2 = 0

Solving
5 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -9x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -9x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x + x2 = 0 + -5
-9x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9x + x2 = -5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + -9x + x2 = 15.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + -4.5 = 3.905124838

Simplifying
x + -4.5 = 3.905124838

Reorder the terms:
-4.5 + x = 3.905124838

Solving
-4.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.905124838 + 4.5
x = 3.905124838 + 4.5

Combine like terms: 3.905124838 + 4.5 = 8.405124838
x = 8.405124838

Simplifying
x = 8.405124838

Subproblem 2
x + -4.5 = -3.905124838

Simplifying
x + -4.5 = -3.905124838

Reorder the terms:
-4.5 + x = -3.905124838

Solving
-4.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.905124838 + 4.5
x = -3.905124838 + 4.5

Combine like terms: -3.905124838 + 4.5 = 0.594875162
x = 0.594875162

Simplifying
x = 0.594875162

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.405124838, 0.594875162}
Solution
x = {8.405124838, 0.594875162}