2x^3-8x^2-72x=0

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Solution for 2x^3-8x^2-72x=0 equation:


Simplifying
2x3 + -8x2 + -72x = 0

Reorder the terms:
-72x + -8x2 + 2x3 = 0

Solving
-72x + -8x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-36 + -4x + x2) = 0

Ignore the factor 2.

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 '(-36 + -4x + x2)' equal to zero and attempt to solve: Simplifying -36 + -4x + x2 = 0 Solving -36 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -4x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -4x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -4x + x2 = 0 + 36 -4x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -4x + x2 = 36 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 36 + 4 Reorder the terms: 4 + -4x + x2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + -4x + x2 = 40 Factor a perfect square on the left side: (x + -2)(x + -2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -2) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + -2 = 6.32455532 Simplifying x + -2 = 6.32455532 Reorder the terms: -2 + x = 6.32455532 Solving -2 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.32455532 + 2 x = 6.32455532 + 2 Combine like terms: 6.32455532 + 2 = 8.32455532 x = 8.32455532 Simplifying x = 8.32455532

Subproblem 2

x + -2 = -6.32455532 Simplifying x + -2 = -6.32455532 Reorder the terms: -2 + x = -6.32455532 Solving -2 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.32455532 + 2 x = -6.32455532 + 2 Combine like terms: -6.32455532 + 2 = -4.32455532 x = -4.32455532 Simplifying x = -4.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.32455532, -4.32455532}

Solution

x = {0, 8.32455532, -4.32455532}

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