3x^3+10x^2-40x=0

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Solution for 3x^3+10x^2-40x=0 equation:


Simplifying
3x3 + 10x2 + -40x = 0

Reorder the terms:
-40x + 10x2 + 3x3 = 0

Solving
-40x + 10x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-40 + 10x + 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 '(-40 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying -40 + 10x + 3x2 = 0 Solving -40 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + 3.333333333x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + 3.333333333x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + 3.333333333x + x2 = 0 + 13.33333333 3.333333333x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 3.333333333x + x2 = 13.33333333 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 13.33333333 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 13.33333333 + 2.777777779 Combine like terms: 13.33333333 + 2.777777779 = 16.111111109 2.777777779 + 3.333333333x + x2 = 16.111111109 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 16.111111109 Calculate the square root of the right side: 4.013864859 Break this problem into two subproblems by setting (x + 1.666666667) equal to 4.013864859 and -4.013864859.

Subproblem 1

x + 1.666666667 = 4.013864859 Simplifying x + 1.666666667 = 4.013864859 Reorder the terms: 1.666666667 + x = 4.013864859 Solving 1.666666667 + x = 4.013864859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 4.013864859 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 4.013864859 + -1.666666667 x = 4.013864859 + -1.666666667 Combine like terms: 4.013864859 + -1.666666667 = 2.347198192 x = 2.347198192 Simplifying x = 2.347198192

Subproblem 2

x + 1.666666667 = -4.013864859 Simplifying x + 1.666666667 = -4.013864859 Reorder the terms: 1.666666667 + x = -4.013864859 Solving 1.666666667 + x = -4.013864859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -4.013864859 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -4.013864859 + -1.666666667 x = -4.013864859 + -1.666666667 Combine like terms: -4.013864859 + -1.666666667 = -5.680531526 x = -5.680531526 Simplifying x = -5.680531526

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.347198192, -5.680531526}

Solution

x = {0, 2.347198192, -5.680531526}

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