x^3-72x^2-30x=0

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Solution for x^3-72x^2-30x=0 equation:


Simplifying
x3 + -72x2 + -30x = 0

Reorder the terms:
-30x + -72x2 + x3 = 0

Solving
-30x + -72x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-30 + -72x + x2) = 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 '(-30 + -72x + x2)' equal to zero and attempt to solve: Simplifying -30 + -72x + x2 = 0 Solving -30 + -72x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -72x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -72x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -72x + x2 = 0 + 30 -72x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -72x + x2 = 30 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = 30 + 1296 Reorder the terms: 1296 + -72x + x2 = 30 + 1296 Combine like terms: 30 + 1296 = 1326 1296 + -72x + x2 = 1326 Factor a perfect square on the left side: (x + -36)(x + -36) = 1326 Calculate the square root of the right side: 36.414282912 Break this problem into two subproblems by setting (x + -36) equal to 36.414282912 and -36.414282912.

Subproblem 1

x + -36 = 36.414282912 Simplifying x + -36 = 36.414282912 Reorder the terms: -36 + x = 36.414282912 Solving -36 + x = 36.414282912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 36.414282912 + 36 Combine like terms: -36 + 36 = 0 0 + x = 36.414282912 + 36 x = 36.414282912 + 36 Combine like terms: 36.414282912 + 36 = 72.414282912 x = 72.414282912 Simplifying x = 72.414282912

Subproblem 2

x + -36 = -36.414282912 Simplifying x + -36 = -36.414282912 Reorder the terms: -36 + x = -36.414282912 Solving -36 + x = -36.414282912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -36.414282912 + 36 Combine like terms: -36 + 36 = 0 0 + x = -36.414282912 + 36 x = -36.414282912 + 36 Combine like terms: -36.414282912 + 36 = -0.414282912 x = -0.414282912 Simplifying x = -0.414282912

Solution

The solution to the problem is based on the solutions from the subproblems. x = {72.414282912, -0.414282912}

Solution

x = {0, 72.414282912, -0.414282912}

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