(x-2)2+7x=(x-3)(x+3)+9

Solution for (x-2)2+7x=(x-3)(x+3)+9 equation:

Simplifying
(x + -2) * 2 + 7x = (x + -3)(x + 3) + 9

Reorder the terms:
(-2 + x) * 2 + 7x = (x + -3)(x + 3) + 9

Reorder the terms for easier multiplication:
2(-2 + x) + 7x = (x + -3)(x + 3) + 9
(-2 * 2 + x * 2) + 7x = (x + -3)(x + 3) + 9
(-4 + 2x) + 7x = (x + -3)(x + 3) + 9

Combine like terms: 2x + 7x = 9x
-4 + 9x = (x + -3)(x + 3) + 9

Reorder the terms:
-4 + 9x = (-3 + x)(x + 3) + 9

Reorder the terms:
-4 + 9x = (-3 + x)(3 + x) + 9

Multiply (-3 + x) * (3 + x)
-4 + 9x = (-3(3 + x) + x(3 + x)) + 9
-4 + 9x = ((3 * -3 + x * -3) + x(3 + x)) + 9
-4 + 9x = ((-9 + -3x) + x(3 + x)) + 9
-4 + 9x = (-9 + -3x + (3 * x + x * x)) + 9
-4 + 9x = (-9 + -3x + (3x + x2)) + 9

Combine like terms: -3x + 3x = 0
-4 + 9x = (-9 + 0 + x2) + 9
-4 + 9x = (-9 + x2) + 9

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

Combine like terms: -9 + 9 = 0
-4 + 9x = 0 + x2
-4 + 9x = x2

Solving
-4 + 9x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-4 + 9x + -1x2 = 0

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

Divide each side by '-1'.
4 + -9x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -9x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -9x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x + x2 = 0 + -4
-9x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-9x + x2 = -4

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -4 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -4 + 20.25

Combine like terms: -4 + 20.25 = 16.25
20.25 + -9x + x2 = 16.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + -4.5 = 4.031128874

Simplifying
x + -4.5 = 4.031128874

Reorder the terms:
-4.5 + x = 4.031128874

Solving
-4.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.031128874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.031128874 + 4.5
x = 4.031128874 + 4.5

Combine like terms: 4.031128874 + 4.5 = 8.531128874
x = 8.531128874

Simplifying
x = 8.531128874

Subproblem 2
x + -4.5 = -4.031128874

Simplifying
x + -4.5 = -4.031128874

Reorder the terms:
-4.5 + x = -4.031128874

Solving
-4.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.031128874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.031128874 + 4.5
x = -4.031128874 + 4.5

Combine like terms: -4.031128874 + 4.5 = 0.468871126
x = 0.468871126

Simplifying
x = 0.468871126

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.531128874, 0.468871126}