(3x-2)(3x-2)=21

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Solution for (3x-2)(3x-2)=21 equation:


Simplifying
(3x + -2)(3x + -2) = 21

Reorder the terms:
(-2 + 3x)(3x + -2) = 21

Reorder the terms:
(-2 + 3x)(-2 + 3x) = 21

Multiply (-2 + 3x) * (-2 + 3x)
(-2(-2 + 3x) + 3x * (-2 + 3x)) = 21
((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 21
((4 + -6x) + 3x * (-2 + 3x)) = 21
(4 + -6x + (-2 * 3x + 3x * 3x)) = 21
(4 + -6x + (-6x + 9x2)) = 21

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = 21

Solving
4 + -12x + 9x2 = 21

Solving for variable 'x'.

Reorder the terms:
4 + -21 + -12x + 9x2 = 21 + -21

Combine like terms: 4 + -21 = -17
-17 + -12x + 9x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-17 + -12x + 9x2 = 0

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

Divide each side by '9'.
-1.888888889 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + -1.333333333x + 1.888888889 + x2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + -1.333333333x + x2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 1.888888889
-1.333333333x + x2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
-1.333333333x + x2 = 1.888888889

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 1.888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 1.888888889 + 0.4444444442

Combine like terms: 1.888888889 + 0.4444444442 = 2.3333333332
0.4444444442 + -1.333333333x + x2 = 2.3333333332

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 2.3333333332

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + -0.6666666665 = 1.527525232 Simplifying x + -0.6666666665 = 1.527525232 Reorder the terms: -0.6666666665 + x = 1.527525232 Solving -0.6666666665 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.527525232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.527525232 + 0.6666666665 x = 1.527525232 + 0.6666666665 Combine like terms: 1.527525232 + 0.6666666665 = 2.1941918985 x = 2.1941918985 Simplifying x = 2.1941918985

Subproblem 2

x + -0.6666666665 = -1.527525232 Simplifying x + -0.6666666665 = -1.527525232 Reorder the terms: -0.6666666665 + x = -1.527525232 Solving -0.6666666665 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.527525232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.527525232 + 0.6666666665 x = -1.527525232 + 0.6666666665 Combine like terms: -1.527525232 + 0.6666666665 = -0.8608585655 x = -0.8608585655 Simplifying x = -0.8608585655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1941918985, -0.8608585655}

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