0=-x^3+15x^2-48x

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Solution for 0=-x^3+15x^2-48x equation:


Simplifying
0 = -1x3 + 15x2 + -48x

Reorder the terms:
0 = -48x + 15x2 + -1x3

Solving
0 = -48x + 15x2 + -1x3

Solving for variable 'x'.
Remove the zero:
48x + -15x2 + x3 = -48x + 15x2 + -1x3 + 48x + -15x2 + x3

Reorder the terms:
48x + -15x2 + x3 = -48x + 48x + 15x2 + -15x2 + -1x3 + x3

Combine like terms: -48x + 48x = 0
48x + -15x2 + x3 = 0 + 15x2 + -15x2 + -1x3 + x3
48x + -15x2 + x3 = 15x2 + -15x2 + -1x3 + x3

Combine like terms: 15x2 + -15x2 = 0
48x + -15x2 + x3 = 0 + -1x3 + x3
48x + -15x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
48x + -15x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(48 + -15x + 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 '(48 + -15x + x2)' equal to zero and attempt to solve: Simplifying 48 + -15x + x2 = 0 Solving 48 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -15x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -15x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -15x + x2 = 0 + -48 -15x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -15x + x2 = -48 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -48 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -48 + 56.25 Combine like terms: -48 + 56.25 = 8.25 56.25 + -15x + x2 = 8.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -7.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + -7.5 = 2.872281323 Simplifying x + -7.5 = 2.872281323 Reorder the terms: -7.5 + x = 2.872281323 Solving -7.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 2.872281323 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 2.872281323 + 7.5 x = 2.872281323 + 7.5 Combine like terms: 2.872281323 + 7.5 = 10.372281323 x = 10.372281323 Simplifying x = 10.372281323

Subproblem 2

x + -7.5 = -2.872281323 Simplifying x + -7.5 = -2.872281323 Reorder the terms: -7.5 + x = -2.872281323 Solving -7.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -2.872281323 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -2.872281323 + 7.5 x = -2.872281323 + 7.5 Combine like terms: -2.872281323 + 7.5 = 4.627718677 x = 4.627718677 Simplifying x = 4.627718677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.372281323, 4.627718677}

Solution

x = {0, 10.372281323, 4.627718677}

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