3(3x-1)(3x-1)=21

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Solution for 3(3x-1)(3x-1)=21 equation:


Simplifying
3(3x + -1)(3x + -1) = 21

Reorder the terms:
3(-1 + 3x)(3x + -1) = 21

Reorder the terms:
3(-1 + 3x)(-1 + 3x) = 21

Multiply (-1 + 3x) * (-1 + 3x)
3(-1(-1 + 3x) + 3x * (-1 + 3x)) = 21
3((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 21
3((1 + -3x) + 3x * (-1 + 3x)) = 21
3(1 + -3x + (-1 * 3x + 3x * 3x)) = 21
3(1 + -3x + (-3x + 9x2)) = 21

Combine like terms: -3x + -3x = -6x
3(1 + -6x + 9x2) = 21
(1 * 3 + -6x * 3 + 9x2 * 3) = 21
(3 + -18x + 27x2) = 21

Solving
3 + -18x + 27x2 = 21

Solving for variable 'x'.

Reorder the terms:
3 + -21 + -18x + 27x2 = 21 + -21

Combine like terms: 3 + -21 = -18
-18 + -18x + 27x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-18 + -18x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + -2x + 3x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(-2 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + -2x + 3x2 = 0 Solving -2 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.6666666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.6666666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + 0.6666666667 -0.6666666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.6666666667x + x2 = 0.6666666667 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 = 0.6666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 0.6666666667 + 0.1111111112 Combine like terms: 0.6666666667 + 0.1111111112 = 0.7777777779 0.1111111112 + -0.6666666667x + x2 = 0.7777777779 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 0.7777777779 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 0.881917104 and -0.881917104.

Subproblem 1

x + -0.3333333334 = 0.881917104 Simplifying x + -0.3333333334 = 0.881917104 Reorder the terms: -0.3333333334 + x = 0.881917104 Solving -0.3333333334 + x = 0.881917104 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 = 0.881917104 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 0.881917104 + 0.3333333334 x = 0.881917104 + 0.3333333334 Combine like terms: 0.881917104 + 0.3333333334 = 1.2152504374 x = 1.2152504374 Simplifying x = 1.2152504374

Subproblem 2

x + -0.3333333334 = -0.881917104 Simplifying x + -0.3333333334 = -0.881917104 Reorder the terms: -0.3333333334 + x = -0.881917104 Solving -0.3333333334 + x = -0.881917104 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 = -0.881917104 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -0.881917104 + 0.3333333334 x = -0.881917104 + 0.3333333334 Combine like terms: -0.881917104 + 0.3333333334 = -0.5485837706 x = -0.5485837706 Simplifying x = -0.5485837706

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2152504374, -0.5485837706}

Solution

x = {1.2152504374, -0.5485837706}

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