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Simplifying 0 = 4x3 + -24x2 + 48x Reorder the terms: 0 = 48x + -24x2 + 4x3 Solving 0 = 48x + -24x2 + 4x3 Solving for variable 'x'. Remove the zero: -48x + 24x2 + -4x3 = 48x + -24x2 + 4x3 + -48x + 24x2 + -4x3 Reorder the terms: -48x + 24x2 + -4x3 = 48x + -48x + -24x2 + 24x2 + 4x3 + -4x3 Combine like terms: 48x + -48x = 0 -48x + 24x2 + -4x3 = 0 + -24x2 + 24x2 + 4x3 + -4x3 -48x + 24x2 + -4x3 = -24x2 + 24x2 + 4x3 + -4x3 Combine like terms: -24x2 + 24x2 = 0 -48x + 24x2 + -4x3 = 0 + 4x3 + -4x3 -48x + 24x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -48x + 24x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-12 + 6x + -1x2) = 0 Ignore the factor 4.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 '(-12 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -12 + 6x + -1x2 = 0 Solving -12 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -6x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -6x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6x + x2 = 0 + -12 -6x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6x + x2 = -12 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -12 + 9 Reorder the terms: 9 + -6x + x2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + -6x + x2 = -3 Factor a perfect square on the left side: (x + -3)(x + -3) = -3 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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