.5x^4+3x^2-2x^3=0

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Solution for .5x^4+3x^2-2x^3=0 equation:


Simplifying
0.5x4 + 3x2 + -2x3 = 0

Reorder the terms:
3x2 + -2x3 + 0.5x4 = 0

Solving
3x2 + -2x3 + 0.5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3 + -2x + 0.5x2) = 0

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(3 + -2x + 0.5x2)' equal to zero and attempt to solve: Simplifying 3 + -2x + 0.5x2 = 0 Solving 3 + -2x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 6 + -4x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -4x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -4x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -4x + x2 = 0 + -6 -4x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -4x + x2 = -6 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -6 + 4 Reorder the terms: 4 + -4x + x2 = -6 + 4 Combine like terms: -6 + 4 = -2 4 + -4x + x2 = -2 Factor a perfect square on the left side: (x + -2)(x + -2) = -2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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