3x^3+3x^2=27x

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Solution for 3x^3+3x^2=27x equation:


Simplifying
3x3 + 3x2 = 27x

Reorder the terms:
3x2 + 3x3 = 27x

Solving
3x2 + 3x3 = 27x

Solving for variable 'x'.

Reorder the terms:
-27x + 3x2 + 3x3 = 27x + -27x

Combine like terms: 27x + -27x = 0
-27x + 3x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + x + x2) = 0

Ignore the factor 3.

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 '(-9 + x + x2)' equal to zero and attempt to solve: Simplifying -9 + x + x2 = 0 Solving -9 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x + x2 = 0 + 9 x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 x + x2 = 9 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 9 + 0.25 Reorder the terms: 0.25 + x + x2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + x + x2 = 9.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 0.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + 0.5 = 3.041381265 Simplifying x + 0.5 = 3.041381265 Reorder the terms: 0.5 + x = 3.041381265 Solving 0.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.041381265 + -0.5 x = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 x = 2.541381265 Simplifying x = 2.541381265

Subproblem 2

x + 0.5 = -3.041381265 Simplifying x + 0.5 = -3.041381265 Reorder the terms: 0.5 + x = -3.041381265 Solving 0.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.041381265 + -0.5 x = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 x = -3.541381265 Simplifying x = -3.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.541381265, -3.541381265}

Solution

x = {0, 2.541381265, -3.541381265}

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