6x^3-2x^2-x=0

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Solution for 6x^3-2x^2-x=0 equation:


Simplifying
6x3 + -2x2 + -1x = 0

Reorder the terms:
-1x + -2x2 + 6x3 = 0

Solving
-1x + -2x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -2x + 6x2) = 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 '(-1 + -2x + 6x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 6x2 = 0 Solving -1 + -2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.3333333333x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.3333333333x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + 0.1666666667 -0.3333333333x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.3333333333x + x2 = 0.1666666667 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.1666666667 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.1666666667 + 0.02777777779 Combine like terms: 0.1666666667 + 0.02777777779 = 0.19444444449 0.02777777779 + -0.3333333333x + x2 = 0.19444444449 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.19444444449 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.440958552 and -0.440958552.

Subproblem 1

x + -0.1666666667 = 0.440958552 Simplifying x + -0.1666666667 = 0.440958552 Reorder the terms: -0.1666666667 + x = 0.440958552 Solving -0.1666666667 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.440958552 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.440958552 + 0.1666666667 x = 0.440958552 + 0.1666666667 Combine like terms: 0.440958552 + 0.1666666667 = 0.6076252187 x = 0.6076252187 Simplifying x = 0.6076252187

Subproblem 2

x + -0.1666666667 = -0.440958552 Simplifying x + -0.1666666667 = -0.440958552 Reorder the terms: -0.1666666667 + x = -0.440958552 Solving -0.1666666667 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.440958552 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.440958552 + 0.1666666667 x = -0.440958552 + 0.1666666667 Combine like terms: -0.440958552 + 0.1666666667 = -0.2742918853 x = -0.2742918853 Simplifying x = -0.2742918853

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6076252187, -0.2742918853}

Solution

x = {0, 0.6076252187, -0.2742918853}

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