8x^3+24x^2-16x=0

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Solution for 8x^3+24x^2-16x=0 equation:


Simplifying
8x3 + 24x2 + -16x = 0

Reorder the terms:
-16x + 24x2 + 8x3 = 0

Solving
-16x + 24x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-2 + 3x + x2) = 0

Ignore the factor 8.

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 '(-2 + 3x + x2)' equal to zero and attempt to solve: Simplifying -2 + 3x + x2 = 0 Solving -2 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + x2 = 0 + 2 3x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3x + x2 = 2 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3x + x2 = 4.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + 1.5 = 2.061552813 Simplifying x + 1.5 = 2.061552813 Reorder the terms: 1.5 + x = 2.061552813 Solving 1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.061552813 + -1.5 x = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 x = 0.561552813 Simplifying x = 0.561552813

Subproblem 2

x + 1.5 = -2.061552813 Simplifying x + 1.5 = -2.061552813 Reorder the terms: 1.5 + x = -2.061552813 Solving 1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.061552813 + -1.5 x = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 x = -3.561552813 Simplifying x = -3.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.561552813, -3.561552813}

Solution

x = {0, 0.561552813, -3.561552813}

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