[x-1]2+[2-x]x=-x+9

Solution for [x-1]2+[2-x]x=-x+9 equation:

Simplifying
[x + -1] * 2 + [2 + -1x] * x = -1x + 9

Reorder the terms:
[-1 + x] * 2 + [2 + -1x] * x = -1x + 9

Reorder the terms for easier multiplication:
2[-1 + x] + [2 + -1x] * x = -1x + 9
[-1 * 2 + x * 2] + [2 + -1x] * x = -1x + 9
[-2 + 2x] + [2 + -1x] * x = -1x + 9

Reorder the terms for easier multiplication:
-2 + 2x + x[2 + -1x] = -1x + 9
-2 + 2x + [2 * x + -1x * x] = -1x + 9
-2 + 2x + [2x + -1x2] = -1x + 9

Combine like terms: 2x + 2x = 4x
-2 + 4x + -1x2 = -1x + 9

Reorder the terms:
-2 + 4x + -1x2 = 9 + -1x

Solving
-2 + 4x + -1x2 = 9 + -1x

Solving for variable 'x'.

Reorder the terms:
-2 + -9 + 4x + x + -1x2 = 9 + -1x + -9 + x

Combine like terms: -2 + -9 = -11
-11 + 4x + x + -1x2 = 9 + -1x + -9 + x

Combine like terms: 4x + x = 5x
-11 + 5x + -1x2 = 9 + -1x + -9 + x

Reorder the terms:
-11 + 5x + -1x2 = 9 + -9 + -1x + x

Combine like terms: 9 + -9 = 0
-11 + 5x + -1x2 = 0 + -1x + x
-11 + 5x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
-11 + 5x + -1x2 = 0

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

Divide each side by '-1'.
11 + -5x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -5x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -5x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5x + x2 = 0 + -11
-5x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-5x + x2 = -11

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -11 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -11 + 6.25

Combine like terms: -11 + 6.25 = -4.75
6.25 + -5x + x2 = -4.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.