3x^3-2x^2-2x=0

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Solution for 3x^3-2x^2-2x=0 equation:


Simplifying
3x3 + -2x2 + -2x = 0

Reorder the terms:
-2x + -2x2 + 3x3 = 0

Solving
-2x + -2x2 + 3x3 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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 = {0, 1.2152504374, -0.5485837706}

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