0.6688=x^2+0.5(1-x)x

Solution for 0.6688=x^2+0.5(1-x)x equation:

Simplifying
0.6688 = x2 + 0.5(1 + -1x) * x

Reorder the terms for easier multiplication:
0.6688 = x2 + 0.5x(1 + -1x)
0.6688 = x2 + (1 * 0.5x + -1x * 0.5x)
0.6688 = x2 + (0.5x + -0.5x2)

Reorder the terms:
0.6688 = 0.5x + x2 + -0.5x2

Combine like terms: x2 + -0.5x2 = 0.5x2
0.6688 = 0.5x + 0.5x2

Solving
0.6688 = 0.5x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
0.6688 + -0.5x + -0.5x2 = 0.5x + -0.5x + 0.5x2 + -0.5x2

Combine like terms: 0.5x + -0.5x = 0.0
0.6688 + -0.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
0.6688 + -0.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
0.6688 + -0.5x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-1.3376 + x + x2 = 0

Move the constant term to the right:

Add '1.3376' to each side of the equation.
-1.3376 + x + 1.3376 + x2 = 0 + 1.3376

Reorder the terms:
-1.3376 + 1.3376 + x + x2 = 0 + 1.3376

Combine like terms: -1.3376 + 1.3376 = 0.0000
0.0000 + x + x2 = 0 + 1.3376
x + x2 = 0 + 1.3376

Combine like terms: 0 + 1.3376 = 1.3376
x + x2 = 1.3376

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.3376 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.3376 + 0.25

Combine like terms: 1.3376 + 0.25 = 1.5876
1.25 + x2 = 1.5876

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.5876

Calculate the square root of the right side: 1.26

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.26 and -1.26.

Subproblem 1
x + 0.5 = 1.26

Simplifying
x + 0.5 = 1.26

Reorder the terms:
0.5 + x = 1.26

Solving
0.5 + x = 1.26

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.26 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.26 + -0.5
x = 1.26 + -0.5

Combine like terms: 1.26 + -0.5 = 0.76
x = 0.76

Simplifying
x = 0.76

Subproblem 2
x + 0.5 = -1.26

Simplifying
x + 0.5 = -1.26

Reorder the terms:
0.5 + x = -1.26

Solving
0.5 + x = -1.26

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.26 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.26 + -0.5
x = -1.26 + -0.5

Combine like terms: -1.26 + -0.5 = -1.76
x = -1.76

Simplifying
x = -1.76

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.76, -1.76}