2(x-3)(x-3)+7=23

Solution for 2(x-3)(x-3)+7=23 equation:

Simplifying
2(x + -3)(x + -3) + 7 = 23

Reorder the terms:
2(-3 + x)(x + -3) + 7 = 23

Reorder the terms:
2(-3 + x)(-3 + x) + 7 = 23

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + 7 = 23
2((-3 * -3 + x * -3) + x(-3 + x)) + 7 = 23
2((9 + -3x) + x(-3 + x)) + 7 = 23
2(9 + -3x + (-3 * x + x * x)) + 7 = 23
2(9 + -3x + (-3x + x2)) + 7 = 23

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + 7 = 23
(9 * 2 + -6x * 2 + x2 * 2) + 7 = 23
(18 + -12x + 2x2) + 7 = 23

Reorder the terms:
18 + 7 + -12x + 2x2 = 23

Combine like terms: 18 + 7 = 25
25 + -12x + 2x2 = 23

Solving
25 + -12x + 2x2 = 23

Solving for variable 'x'.

Reorder the terms:
25 + -23 + -12x + 2x2 = 23 + -23

Combine like terms: 25 + -23 = 2
2 + -12x + 2x2 = 23 + -23

Combine like terms: 23 + -23 = 0
2 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x + x2 = 0

Solving
1 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -6x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x + x2 = 0 + -1
-6x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6x + x2 = -1

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1 + 9

Reorder the terms:
9 + -6x + x2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + -6x + x2 = 8

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -3) equal to 2.828427125 and -2.828427125.

Subproblem 1
x + -3 = 2.828427125

Simplifying
x + -3 = 2.828427125

Reorder the terms:
-3 + x = 2.828427125

Solving
-3 + x = 2.828427125

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.828427125 + 3
x = 2.828427125 + 3

Combine like terms: 2.828427125 + 3 = 5.828427125
x = 5.828427125

Simplifying
x = 5.828427125

Subproblem 2
x + -3 = -2.828427125

Simplifying
x + -3 = -2.828427125

Reorder the terms:
-3 + x = -2.828427125

Solving
-3 + x = -2.828427125

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.828427125 + 3
x = -2.828427125 + 3

Combine like terms: -2.828427125 + 3 = 0.171572875
x = 0.171572875

Simplifying
x = 0.171572875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.828427125, 0.171572875}
Solution
x = {5.828427125, 0.171572875}