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

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


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

Multiply (2 + -3x) * (2 + -3x)
(2(2 + -3x) + -3x * (2 + -3x)) = 8
((2 * 2 + -3x * 2) + -3x * (2 + -3x)) = 8
((4 + -6x) + -3x * (2 + -3x)) = 8
(4 + -6x + (2 * -3x + -3x * -3x)) = 8
(4 + -6x + (-6x + 9x2)) = 8

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) = 8

Solving
4 + -12x + 9x2 = 8

Solving for variable 'x'.

Reorder the terms:
4 + -8 + -12x + 9x2 = 8 + -8

Combine like terms: 4 + -8 = -4
-4 + -12x + 9x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-4 + -12x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -1.333333333x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -1.333333333x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.4444444444
-1.333333333x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-1.333333333x + x2 = 0.4444444444

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 = 0.4444444444 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.4444444444 + 0.4444444442

Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886
0.4444444442 + -1.333333333x + x2 = 0.8888888886

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.8888888886

Calculate the square root of the right side: 0.942809041

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.942809041 and -0.942809041.

Subproblem 1

x + -0.6666666665 = 0.942809041 Simplifying x + -0.6666666665 = 0.942809041 Reorder the terms: -0.6666666665 + x = 0.942809041 Solving -0.6666666665 + x = 0.942809041 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 = 0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.942809041 + 0.6666666665 x = 0.942809041 + 0.6666666665 Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075 x = 1.6094757075 Simplifying x = 1.6094757075

Subproblem 2

x + -0.6666666665 = -0.942809041 Simplifying x + -0.6666666665 = -0.942809041 Reorder the terms: -0.6666666665 + x = -0.942809041 Solving -0.6666666665 + x = -0.942809041 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 = -0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.942809041 + 0.6666666665 x = -0.942809041 + 0.6666666665 Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745 x = -0.2761423745 Simplifying x = -0.2761423745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.6094757075, -0.2761423745}

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