k^3-4k^2-19k=0

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Solution for k^3-4k^2-19k=0 equation:


Simplifying
k3 + -4k2 + -19k = 0

Reorder the terms:
-19k + -4k2 + k3 = 0

Solving
-19k + -4k2 + k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-19 + -4k + k2) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(-19 + -4k + k2)' equal to zero and attempt to solve: Simplifying -19 + -4k + k2 = 0 Solving -19 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -4k + 19 + k2 = 0 + 19 Reorder the terms: -19 + 19 + -4k + k2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4k + k2 = 0 + 19 -4k + k2 = 0 + 19 Combine like terms: 0 + 19 = 19 -4k + k2 = 19 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 19 + 4 Reorder the terms: 4 + -4k + k2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + -4k + k2 = 23 Factor a perfect square on the left side: (k + -2)(k + -2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (k + -2) equal to 4.795831523 and -4.795831523.

Subproblem 1

k + -2 = 4.795831523 Simplifying k + -2 = 4.795831523 Reorder the terms: -2 + k = 4.795831523 Solving -2 + k = 4.795831523 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + k = 4.795831523 + 2 k = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 k = 6.795831523 Simplifying k = 6.795831523

Subproblem 2

k + -2 = -4.795831523 Simplifying k + -2 = -4.795831523 Reorder the terms: -2 + k = -4.795831523 Solving -2 + k = -4.795831523 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + k = -4.795831523 + 2 k = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 k = -2.795831523 Simplifying k = -2.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. k = {6.795831523, -2.795831523}

Solution

k = {0, 6.795831523, -2.795831523}

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