2(x-3)(x-3)=-2x+9

Solution for 2(x-3)(x-3)=-2x+9 equation:

Simplifying
2(x + -3)(x + -3) = -2x + 9

Reorder the terms:
2(-3 + x)(x + -3) = -2x + 9

Reorder the terms:
2(-3 + x)(-3 + x) = -2x + 9

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) = -2x + 9
2((-3 * -3 + x * -3) + x(-3 + x)) = -2x + 9
2((9 + -3x) + x(-3 + x)) = -2x + 9
2(9 + -3x + (-3 * x + x * x)) = -2x + 9
2(9 + -3x + (-3x + x2)) = -2x + 9

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) = -2x + 9
(9 * 2 + -6x * 2 + x2 * 2) = -2x + 9
(18 + -12x + 2x2) = -2x + 9

Reorder the terms:
18 + -12x + 2x2 = 9 + -2x

Solving
18 + -12x + 2x2 = 9 + -2x

Solving for variable 'x'.

Reorder the terms:
18 + -9 + -12x + 2x + 2x2 = 9 + -2x + -9 + 2x

Combine like terms: 18 + -9 = 9
9 + -12x + 2x + 2x2 = 9 + -2x + -9 + 2x

Combine like terms: -12x + 2x = -10x
9 + -10x + 2x2 = 9 + -2x + -9 + 2x

Reorder the terms:
9 + -10x + 2x2 = 9 + -9 + -2x + 2x

Combine like terms: 9 + -9 = 0
9 + -10x + 2x2 = 0 + -2x + 2x
9 + -10x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
9 + -10x + 2x2 = 0

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

Divide each side by '2'.
4.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -5x + x2 = 0 + -4.5
-5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-5x + x2 = -4.5

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 = -4.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + -5x + x2 = 1.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
x + -2.5 = 1.322875656

Simplifying
x + -2.5 = 1.322875656

Reorder the terms:
-2.5 + x = 1.322875656

Solving
-2.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.322875656 + 2.5
x = 1.322875656 + 2.5

Combine like terms: 1.322875656 + 2.5 = 3.822875656
x = 3.822875656

Simplifying
x = 3.822875656

Subproblem 2
x + -2.5 = -1.322875656

Simplifying
x + -2.5 = -1.322875656

Reorder the terms:
-2.5 + x = -1.322875656

Solving
-2.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.322875656 + 2.5
x = -1.322875656 + 2.5

Combine like terms: -1.322875656 + 2.5 = 1.177124344
x = 1.177124344

Simplifying
x = 1.177124344

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.822875656, 1.177124344}