-x^2+2x-0.96=0

Solution for -x^2+2x-0.96=0 equation:

Simplifying
-1x2 + 2x + -0.96 = 0

Reorder the terms:
-0.96 + 2x + -1x2 = 0

Solving
-0.96 + 2x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
0.96 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.96' to each side of the equation.
0.96 + -2x + -0.96 + x2 = 0 + -0.96

Reorder the terms:
0.96 + -0.96 + -2x + x2 = 0 + -0.96

Combine like terms: 0.96 + -0.96 = 0.00
0.00 + -2x + x2 = 0 + -0.96
-2x + x2 = 0 + -0.96

Combine like terms: 0 + -0.96 = -0.96
-2x + x2 = -0.96

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.96 + 1

Reorder the terms:
1 + -2x + x2 = -0.96 + 1

Combine like terms: -0.96 + 1 = 0.04
1 + -2x + x2 = 0.04

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -1) equal to 0.2 and -0.2.

Subproblem 1
x + -1 = 0.2

Simplifying
x + -1 = 0.2

Reorder the terms:
-1 + x = 0.2

Solving
-1 + x = 0.2

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.2 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.2 + 1
x = 0.2 + 1

Combine like terms: 0.2 + 1 = 1.2
x = 1.2

Simplifying
x = 1.2

Subproblem 2
x + -1 = -0.2

Simplifying
x + -1 = -0.2

Reorder the terms:
-1 + x = -0.2

Solving
-1 + x = -0.2

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.2 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.2 + 1
x = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
x = 0.8

Simplifying
x = 0.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, 0.8}