(3x-1)(3x-1)=28

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Solution for (3x-1)(3x-1)=28 equation:


Simplifying
(3x + -1)(3x + -1) = 28

Reorder the terms:
(-1 + 3x)(3x + -1) = 28

Reorder the terms:
(-1 + 3x)(-1 + 3x) = 28

Multiply (-1 + 3x) * (-1 + 3x)
(-1(-1 + 3x) + 3x * (-1 + 3x)) = 28
((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 28
((1 + -3x) + 3x * (-1 + 3x)) = 28
(1 + -3x + (-1 * 3x + 3x * 3x)) = 28
(1 + -3x + (-3x + 9x2)) = 28

Combine like terms: -3x + -3x = -6x
(1 + -6x + 9x2) = 28

Solving
1 + -6x + 9x2 = 28

Solving for variable 'x'.

Reorder the terms:
1 + -28 + -6x + 9x2 = 28 + -28

Combine like terms: 1 + -28 = -27
-27 + -6x + 9x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-27 + -6x + 9x2 = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-9 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + -2x + 3x2 = 0 Solving -9 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.6666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.6666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.6666666667x + x2 = 0 + 3 -0.6666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.6666666667x + x2 = 3 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 = 3 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 3 + 0.1111111112 Combine like terms: 3 + 0.1111111112 = 3.1111111112 0.1111111112 + -0.6666666667x + x2 = 3.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 3.1111111112 Calculate the square root of the right side: 1.763834207 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.763834207 and -1.763834207.

Subproblem 1

x + -0.3333333334 = 1.763834207 Simplifying x + -0.3333333334 = 1.763834207 Reorder the terms: -0.3333333334 + x = 1.763834207 Solving -0.3333333334 + x = 1.763834207 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 = 1.763834207 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.763834207 + 0.3333333334 x = 1.763834207 + 0.3333333334 Combine like terms: 1.763834207 + 0.3333333334 = 2.0971675404 x = 2.0971675404 Simplifying x = 2.0971675404

Subproblem 2

x + -0.3333333334 = -1.763834207 Simplifying x + -0.3333333334 = -1.763834207 Reorder the terms: -0.3333333334 + x = -1.763834207 Solving -0.3333333334 + x = -1.763834207 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 = -1.763834207 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.763834207 + 0.3333333334 x = -1.763834207 + 0.3333333334 Combine like terms: -1.763834207 + 0.3333333334 = -1.4305008736 x = -1.4305008736 Simplifying x = -1.4305008736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.0971675404, -1.4305008736}

Solution

x = {2.0971675404, -1.4305008736}

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