8x^3-5x^2-16x=0

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Solution for 8x^3-5x^2-16x=0 equation:


Simplifying
8x3 + -5x2 + -16x = 0

Reorder the terms:
-16x + -5x2 + 8x3 = 0

Solving
-16x + -5x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-16 + -5x + 8x2) = 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 '(-16 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying -16 + -5x + 8x2 = 0 Solving -16 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + -0.625x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.625x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.625x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.625x + x2 = 0 + 2 -0.625x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.625x + x2 = 2 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 2 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 2 + 0.09765625 Combine like terms: 2 + 0.09765625 = 2.09765625 0.09765625 + -0.625x + x2 = 2.09765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 2.09765625 Calculate the square root of the right side: 1.448328778 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.448328778 and -1.448328778.

Subproblem 1

x + -0.3125 = 1.448328778 Simplifying x + -0.3125 = 1.448328778 Reorder the terms: -0.3125 + x = 1.448328778 Solving -0.3125 + x = 1.448328778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.448328778 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.448328778 + 0.3125 x = 1.448328778 + 0.3125 Combine like terms: 1.448328778 + 0.3125 = 1.760828778 x = 1.760828778 Simplifying x = 1.760828778

Subproblem 2

x + -0.3125 = -1.448328778 Simplifying x + -0.3125 = -1.448328778 Reorder the terms: -0.3125 + x = -1.448328778 Solving -0.3125 + x = -1.448328778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.448328778 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.448328778 + 0.3125 x = -1.448328778 + 0.3125 Combine like terms: -1.448328778 + 0.3125 = -1.135828778 x = -1.135828778 Simplifying x = -1.135828778

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.760828778, -1.135828778}

Solution

x = {0, 1.760828778, -1.135828778}

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