(3x-5)*(3x-5)=7

Solution for (3x-5)*(3x-5)=7 equation:

Simplifying
(3x + -5)(3x + -5) = 7

Reorder the terms:
(-5 + 3x)(3x + -5) = 7

Reorder the terms:
(-5 + 3x)(-5 + 3x) = 7

Multiply (-5 + 3x) * (-5 + 3x)
(-5(-5 + 3x) + 3x * (-5 + 3x)) = 7
((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) = 7
((25 + -15x) + 3x * (-5 + 3x)) = 7
(25 + -15x + (-5 * 3x + 3x * 3x)) = 7
(25 + -15x + (-15x + 9x2)) = 7

Combine like terms: -15x + -15x = -30x
(25 + -30x + 9x2) = 7

Solving
25 + -30x + 9x2 = 7

Solving for variable 'x'.

Reorder the terms:
25 + -7 + -30x + 9x2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + -30x + 9x2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + -30x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -10x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + -10x + 3x2 = 0

Solving
6 + -10x + 3x2 = 0

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

Divide each side by '3'.
2 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.333333333x + x2 = 0 + -2
-3.333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.333333333x + x2 = -2

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -2 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -2 + 2.777777779

Combine like terms: -2 + 2.777777779 = 0.777777779
2.777777779 + -3.333333333x + x2 = 0.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 0.777777779

Calculate the square root of the right side: 0.881917104

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 0.881917104 and -0.881917104.

Subproblem 1
x + -1.666666667 = 0.881917104

Simplifying
x + -1.666666667 = 0.881917104

Reorder the terms:
-1.666666667 + x = 0.881917104

Solving
-1.666666667 + x = 0.881917104

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 0.881917104 + 1.666666667
x = 0.881917104 + 1.666666667

Combine like terms: 0.881917104 + 1.666666667 = 2.548583771
x = 2.548583771

Simplifying
x = 2.548583771

Subproblem 2
x + -1.666666667 = -0.881917104

Simplifying
x + -1.666666667 = -0.881917104

Reorder the terms:
-1.666666667 + x = -0.881917104

Solving
-1.666666667 + x = -0.881917104

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -0.881917104 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -0.881917104 + 1.666666667
x = -0.881917104 + 1.666666667

Combine like terms: -0.881917104 + 1.666666667 = 0.784749563
x = 0.784749563

Simplifying
x = 0.784749563

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.548583771, 0.784749563}
Solution
x = {2.548583771, 0.784749563}