-2x^2+20x=10

Solution for -2x^2+20x=10 equation:

Simplifying
-2x2 + 20x = 10

Reorder the terms:
20x + -2x2 = 10

Solving
20x + -2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 20x + -2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 10x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 10x + -1x2 = 0

Solving
-5 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -10x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -10x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10x + x2 = 0 + -5
-10x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10x + x2 = -5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -5 + 25

Reorder the terms:
25 + -10x + x2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10x + x2 = 20

Factor a perfect square on the left side:
(x + -5)(x + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -5) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + -5 = 4.472135955

Simplifying
x + -5 = 4.472135955

Reorder the terms:
-5 + x = 4.472135955

Solving
-5 + x = 4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.472135955 + 5
x = 4.472135955 + 5

Combine like terms: 4.472135955 + 5 = 9.472135955
x = 9.472135955

Simplifying
x = 9.472135955

Subproblem 2
x + -5 = -4.472135955

Simplifying
x + -5 = -4.472135955

Reorder the terms:
-5 + x = -4.472135955

Solving
-5 + x = -4.472135955

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.472135955 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.472135955 + 5
x = -4.472135955 + 5

Combine like terms: -4.472135955 + 5 = 0.527864045
x = 0.527864045

Simplifying
x = 0.527864045

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.472135955, 0.527864045}
Solution
x = {9.472135955, 0.527864045}