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Simplifying 0 = 48x3 + -24x2 + 48x Reorder the terms: 0 = 48x + -24x2 + 48x3 Solving 0 = 48x + -24x2 + 48x3 Solving for variable 'x'. Remove the zero: -48x + 24x2 + -48x3 = 48x + -24x2 + 48x3 + -48x + 24x2 + -48x3 Reorder the terms: -48x + 24x2 + -48x3 = 48x + -48x + -24x2 + 24x2 + 48x3 + -48x3 Combine like terms: 48x + -48x = 0 -48x + 24x2 + -48x3 = 0 + -24x2 + 24x2 + 48x3 + -48x3 -48x + 24x2 + -48x3 = -24x2 + 24x2 + 48x3 + -48x3 Combine like terms: -24x2 + 24x2 = 0 -48x + 24x2 + -48x3 = 0 + 48x3 + -48x3 -48x + 24x2 + -48x3 = 48x3 + -48x3 Combine like terms: 48x3 + -48x3 = 0 -48x + 24x2 + -48x3 = 0 Factor out the Greatest Common Factor (GCF), '24x'. 24x(-2 + x + -2x2) = 0 Ignore the factor 24.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 = 0Subproblem 2
Set the factor '(-2 + x + -2x2)' equal to zero and attempt to solve: Simplifying -2 + x + -2x2 = 0 Solving -2 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.5x + x2 = 0 + -1 -0.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.5x + x2 = -1 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. -0.5x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -0.5x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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