2x^3+3x^2-366x=0

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Solution for 2x^3+3x^2-366x=0 equation:


Simplifying
2x3 + 3x2 + -366x = 0

Reorder the terms:
-366x + 3x2 + 2x3 = 0

Solving
-366x + 3x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-366 + 3x + 2x2) = 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 '(-366 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -366 + 3x + 2x2 = 0 Solving -366 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -183 + 1.5x + x2 = 0 Move the constant term to the right: Add '183' to each side of the equation. -183 + 1.5x + 183 + x2 = 0 + 183 Reorder the terms: -183 + 183 + 1.5x + x2 = 0 + 183 Combine like terms: -183 + 183 = 0 0 + 1.5x + x2 = 0 + 183 1.5x + x2 = 0 + 183 Combine like terms: 0 + 183 = 183 1.5x + x2 = 183 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 183 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 183 + 0.5625 Combine like terms: 183 + 0.5625 = 183.5625 0.5625 + 1.5x + x2 = 183.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 183.5625 Calculate the square root of the right side: 13.548523905 Break this problem into two subproblems by setting (x + 0.75) equal to 13.548523905 and -13.548523905.

Subproblem 1

x + 0.75 = 13.548523905 Simplifying x + 0.75 = 13.548523905 Reorder the terms: 0.75 + x = 13.548523905 Solving 0.75 + x = 13.548523905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 13.548523905 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 13.548523905 + -0.75 x = 13.548523905 + -0.75 Combine like terms: 13.548523905 + -0.75 = 12.798523905 x = 12.798523905 Simplifying x = 12.798523905

Subproblem 2

x + 0.75 = -13.548523905 Simplifying x + 0.75 = -13.548523905 Reorder the terms: 0.75 + x = -13.548523905 Solving 0.75 + x = -13.548523905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -13.548523905 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -13.548523905 + -0.75 x = -13.548523905 + -0.75 Combine like terms: -13.548523905 + -0.75 = -14.298523905 x = -14.298523905 Simplifying x = -14.298523905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.798523905, -14.298523905}

Solution

x = {0, 12.798523905, -14.298523905}

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