2(x-3)(x-3)-5=0

Solution for 2(x-3)(x-3)-5=0 equation:

Simplifying
2(x + -3)(x + -3) + -5 = 0

Reorder the terms:
2(-3 + x)(x + -3) + -5 = 0

Reorder the terms:
2(-3 + x)(-3 + x) + -5 = 0

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) + -5 = 0
2((-3 * -3 + x * -3) + x(-3 + x)) + -5 = 0
2((9 + -3x) + x(-3 + x)) + -5 = 0
2(9 + -3x + (-3 * x + x * x)) + -5 = 0
2(9 + -3x + (-3x + x2)) + -5 = 0

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) + -5 = 0
(9 * 2 + -6x * 2 + x2 * 2) + -5 = 0
(18 + -12x + 2x2) + -5 = 0

Reorder the terms:
18 + -5 + -12x + 2x2 = 0

Combine like terms: 18 + -5 = 13
13 + -12x + 2x2 = 0

Solving
13 + -12x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
6.5 + -6x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -6x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -6x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -6x + x2 = 0 + -6.5
-6x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-6x + x2 = -6.5

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 = -6.5 + 9

Reorder the terms:
9 + -6x + x2 = -6.5 + 9

Combine like terms: -6.5 + 9 = 2.5
9 + -6x + x2 = 2.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -3) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -3 = 1.58113883

Simplifying
x + -3 = 1.58113883

Reorder the terms:
-3 + x = 1.58113883

Solving
-3 + x = 1.58113883

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 = 1.58113883 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.58113883 + 3
x = 1.58113883 + 3

Combine like terms: 1.58113883 + 3 = 4.58113883
x = 4.58113883

Simplifying
x = 4.58113883

Subproblem 2
x + -3 = -1.58113883

Simplifying
x + -3 = -1.58113883

Reorder the terms:
-3 + x = -1.58113883

Solving
-3 + x = -1.58113883

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 = -1.58113883 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.58113883 + 3
x = -1.58113883 + 3

Combine like terms: -1.58113883 + 3 = 1.41886117
x = 1.41886117

Simplifying
x = 1.41886117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.58113883, 1.41886117}