3(x-3)(x-3)+2=8

Solution for 3(x-3)(x-3)+2=8 equation:

Simplifying
3(x + -3)(x + -3) + 2 = 8

Reorder the terms:
3(-3 + x)(x + -3) + 2 = 8

Reorder the terms:
3(-3 + x)(-3 + x) + 2 = 8

Multiply (-3 + x) * (-3 + x)
3(-3(-3 + x) + x(-3 + x)) + 2 = 8
3((-3 * -3 + x * -3) + x(-3 + x)) + 2 = 8
3((9 + -3x) + x(-3 + x)) + 2 = 8
3(9 + -3x + (-3 * x + x * x)) + 2 = 8
3(9 + -3x + (-3x + x2)) + 2 = 8

Combine like terms: -3x + -3x = -6x
3(9 + -6x + x2) + 2 = 8
(9 * 3 + -6x * 3 + x2 * 3) + 2 = 8
(27 + -18x + 3x2) + 2 = 8

Reorder the terms:
27 + 2 + -18x + 3x2 = 8

Combine like terms: 27 + 2 = 29
29 + -18x + 3x2 = 8

Solving
29 + -18x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
29 + -8 + -18x + 3x2 = 8 + -8

Combine like terms: 29 + -8 = 21
21 + -18x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
21 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -6x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x + x2 = 0

Solving
7 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x + x2 = 0 + -7
-6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6x + x2 = -7

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 = -7 + 9

Reorder the terms:
9 + -6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6x + x2 = 2

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -3) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -3 = 1.414213562

Simplifying
x + -3 = 1.414213562

Reorder the terms:
-3 + x = 1.414213562

Solving
-3 + x = 1.414213562

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 = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.414213562 + 3
x = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
x = 4.414213562

Simplifying
x = 4.414213562

Subproblem 2
x + -3 = -1.414213562

Simplifying
x + -3 = -1.414213562

Reorder the terms:
-3 + x = -1.414213562

Solving
-3 + x = -1.414213562

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 = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.414213562 + 3
x = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
x = 1.585786438

Simplifying
x = 1.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.414213562, 1.585786438}
Solution
x = {4.414213562, 1.585786438}