A^3+5A=15A^2

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Solution for A^3+5A=15A^2 equation:


Simplifying
A3 + 5A = 15A2

Reorder the terms:
5A + A3 = 15A2

Solving
5A + A3 = 15A2

Solving for variable 'A'.

Reorder the terms:
5A + -15A2 + A3 = 15A2 + -15A2

Combine like terms: 15A2 + -15A2 = 0
5A + -15A2 + A3 = 0

Factor out the Greatest Common Factor (GCF), 'A'.
A(5 + -15A + A2) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -15A + A2)' equal to zero and attempt to solve: Simplifying 5 + -15A + A2 = 0 Solving 5 + -15A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -15A + -5 + A2 = 0 + -5 Reorder the terms: 5 + -5 + -15A + A2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -15A + A2 = 0 + -5 -15A + A2 = 0 + -5 Combine like terms: 0 + -5 = -5 -15A + A2 = -5 The A term is -15A. 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. -15A + 56.25 + A2 = -5 + 56.25 Reorder the terms: 56.25 + -15A + A2 = -5 + 56.25 Combine like terms: -5 + 56.25 = 51.25 56.25 + -15A + A2 = 51.25 Factor a perfect square on the left side: (A + -7.5)(A + -7.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (A + -7.5) equal to 7.158910532 and -7.158910532.

Subproblem 1

A + -7.5 = 7.158910532 Simplifying A + -7.5 = 7.158910532 Reorder the terms: -7.5 + A = 7.158910532 Solving -7.5 + A = 7.158910532 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + A = 7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + A = 7.158910532 + 7.5 A = 7.158910532 + 7.5 Combine like terms: 7.158910532 + 7.5 = 14.658910532 A = 14.658910532 Simplifying A = 14.658910532

Subproblem 2

A + -7.5 = -7.158910532 Simplifying A + -7.5 = -7.158910532 Reorder the terms: -7.5 + A = -7.158910532 Solving -7.5 + A = -7.158910532 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + A = -7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + A = -7.158910532 + 7.5 A = -7.158910532 + 7.5 Combine like terms: -7.158910532 + 7.5 = 0.341089468 A = 0.341089468 Simplifying A = 0.341089468

Solution

The solution to the problem is based on the solutions from the subproblems. A = {14.658910532, 0.341089468}

Solution

A = {0, 14.658910532, 0.341089468}

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