(3x-2)(x-2)=36

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Solution for (3x-2)(x-2)=36 equation:


Simplifying
(3x + -2)(x + -2) = 36

Reorder the terms:
(-2 + 3x)(x + -2) = 36

Reorder the terms:
(-2 + 3x)(-2 + x) = 36

Multiply (-2 + 3x) * (-2 + x)
(-2(-2 + x) + 3x * (-2 + x)) = 36
((-2 * -2 + x * -2) + 3x * (-2 + x)) = 36
((4 + -2x) + 3x * (-2 + x)) = 36
(4 + -2x + (-2 * 3x + x * 3x)) = 36
(4 + -2x + (-6x + 3x2)) = 36

Combine like terms: -2x + -6x = -8x
(4 + -8x + 3x2) = 36

Solving
4 + -8x + 3x2 = 36

Solving for variable 'x'.

Reorder the terms:
4 + -36 + -8x + 3x2 = 36 + -36

Combine like terms: 4 + -36 = -32
-32 + -8x + 3x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-32 + -8x + 3x2 = 0

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

Divide each side by '3'.
-10.66666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + -2.666666667x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + -2.666666667x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + -2.666666667x + x2 = 0 + 10.66666667
-2.666666667x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
-2.666666667x + x2 = 10.66666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 10.66666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 10.66666667 + 1.777777780

Combine like terms: 10.66666667 + 1.777777780 = 12.44444445
1.777777780 + -2.666666667x + x2 = 12.44444445

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 12.44444445

Calculate the square root of the right side: 3.527668416

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 3.527668416 and -3.527668416.

Subproblem 1

x + -1.333333334 = 3.527668416 Simplifying x + -1.333333334 = 3.527668416 Reorder the terms: -1.333333334 + x = 3.527668416 Solving -1.333333334 + x = 3.527668416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 3.527668416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 3.527668416 + 1.333333334 x = 3.527668416 + 1.333333334 Combine like terms: 3.527668416 + 1.333333334 = 4.86100175 x = 4.86100175 Simplifying x = 4.86100175

Subproblem 2

x + -1.333333334 = -3.527668416 Simplifying x + -1.333333334 = -3.527668416 Reorder the terms: -1.333333334 + x = -3.527668416 Solving -1.333333334 + x = -3.527668416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -3.527668416 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -3.527668416 + 1.333333334 x = -3.527668416 + 1.333333334 Combine like terms: -3.527668416 + 1.333333334 = -2.194335082 x = -2.194335082 Simplifying x = -2.194335082

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.86100175, -2.194335082}

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