3x^3+2x^2-41x=0

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Solution for 3x^3+2x^2-41x=0 equation:


Simplifying
3x3 + 2x2 + -41x = 0

Reorder the terms:
-41x + 2x2 + 3x3 = 0

Solving
-41x + 2x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-41 + 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 '(-41 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -41 + 2x + 3x2 = 0 Solving -41 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.66666667 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '13.66666667' to each side of the equation. -13.66666667 + 0.6666666667x + 13.66666667 + x2 = 0 + 13.66666667 Reorder the terms: -13.66666667 + 13.66666667 + 0.6666666667x + x2 = 0 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + 0.6666666667x + x2 = 0 + 13.66666667 0.6666666667x + x2 = 0 + 13.66666667 Combine like terms: 0 + 13.66666667 = 13.66666667 0.6666666667x + x2 = 13.66666667 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 = 13.66666667 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 13.66666667 + 0.1111111112 Combine like terms: 13.66666667 + 0.1111111112 = 13.7777777812 0.1111111112 + 0.6666666667x + x2 = 13.7777777812 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 13.7777777812 Calculate the square root of the right side: 3.711842909 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.711842909 and -3.711842909.

Subproblem 1

x + 0.3333333334 = 3.711842909 Simplifying x + 0.3333333334 = 3.711842909 Reorder the terms: 0.3333333334 + x = 3.711842909 Solving 0.3333333334 + x = 3.711842909 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 = 3.711842909 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.711842909 + -0.3333333334 x = 3.711842909 + -0.3333333334 Combine like terms: 3.711842909 + -0.3333333334 = 3.3785095756 x = 3.3785095756 Simplifying x = 3.3785095756

Subproblem 2

x + 0.3333333334 = -3.711842909 Simplifying x + 0.3333333334 = -3.711842909 Reorder the terms: 0.3333333334 + x = -3.711842909 Solving 0.3333333334 + x = -3.711842909 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 = -3.711842909 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.711842909 + -0.3333333334 x = -3.711842909 + -0.3333333334 Combine like terms: -3.711842909 + -0.3333333334 = -4.0451762424 x = -4.0451762424 Simplifying x = -4.0451762424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.3785095756, -4.0451762424}

Solution

x = {0, 3.3785095756, -4.0451762424}

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