(3x-1)(3x-1)=22

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Solution for (3x-1)(3x-1)=22 equation: 


Simplifying
(3x + -1)(3x + -1) = 22

Reorder the terms:
(-1 + 3x)(3x + -1) = 22

Reorder the terms:
(-1 + 3x)(-1 + 3x) = 22

Multiply (-1 + 3x) * (-1 + 3x)
(-1(-1 + 3x) + 3x * (-1 + 3x)) = 22
((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 22
((1 + -3x) + 3x * (-1 + 3x)) = 22
(1 + -3x + (-1 * 3x + 3x * 3x)) = 22
(1 + -3x + (-3x + 9x2)) = 22

Combine like terms: -3x + -3x = -6x
(1 + -6x + 9x2) = 22

Solving
1 + -6x + 9x2 = 22

Solving for variable 'x'.

Reorder the terms:
1 + -22 + -6x + 9x2 = 22 + -22

Combine like terms: 1 + -22 = -21
-21 + -6x + 9x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-21 + -6x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -2x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-7 + -2x + 3x2 = 0

Solving
-7 + -2x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -0.6666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -0.6666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 2.333333333
-0.6666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-0.6666666667x + x2 = 2.333333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 2.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2.333333333 + 0.1111111112

Combine like terms: 2.333333333 + 0.1111111112 = 2.4444444442
0.1111111112 + -0.6666666667x + x2 = 2.4444444442

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.56347192 and -1.56347192.


Subproblem 1
x + -0.3333333334 = 1.56347192

Simplifying
x + -0.3333333334 = 1.56347192

Reorder the terms:
-0.3333333334 + x = 1.56347192

Solving
-0.3333333334 + x = 1.56347192

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.56347192 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.56347192 + 0.3333333334
x = 1.56347192 + 0.3333333334

Combine like terms: 1.56347192 + 0.3333333334 = 1.8968052534
x = 1.8968052534

Simplifying
x = 1.8968052534


Subproblem 2
x + -0.3333333334 = -1.56347192

Simplifying
x + -0.3333333334 = -1.56347192

Reorder the terms:
-0.3333333334 + x = -1.56347192

Solving
-0.3333333334 + x = -1.56347192

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.56347192 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.56347192 + 0.3333333334
x = -1.56347192 + 0.3333333334

Combine like terms: -1.56347192 + 0.3333333334 = -1.2301385866
x = -1.2301385866

Simplifying
x = -1.2301385866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8968052534, -1.2301385866}
Solution
x = {1.8968052534, -1.2301385866}

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