0=-2x^2+20x-2

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


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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor 2.

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

Simplifying
1 + -10x + x2 = 0

Solving
1 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -10x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x + x2 = 0 + -1
-10x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10x + x2 = -1

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 = -1 + 25

Reorder the terms:
25 + -10x + x2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + -10x + x2 = 24

Factor a perfect square on the left side:
(x + -5)(x + -5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -5) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + -5 = 4.898979486

Simplifying
x + -5 = 4.898979486

Reorder the terms:
-5 + x = 4.898979486

Solving
-5 + x = 4.898979486

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 = 4.898979486 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.898979486 + 5
x = 4.898979486 + 5

Combine like terms: 4.898979486 + 5 = 9.898979486
x = 9.898979486

Simplifying
x = 9.898979486


Subproblem 2
x + -5 = -4.898979486

Simplifying
x + -5 = -4.898979486

Reorder the terms:
-5 + x = -4.898979486

Solving
-5 + x = -4.898979486

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 = -4.898979486 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.898979486 + 5
x = -4.898979486 + 5

Combine like terms: -4.898979486 + 5 = 0.101020514
x = 0.101020514

Simplifying
x = 0.101020514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.898979486, 0.101020514}
Solution
x = {9.898979486, 0.101020514}

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