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Simplifying -2x3 + 10x2 + -16x = 0 Reorder the terms: -16x + 10x2 + -2x3 = 0 Solving -16x + 10x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + 5x + -1x2) = 0 Ignore the factor 2.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 '(-8 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 5x + -1x2 = 0 Solving -8 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x + x2 = 0 + -8 -5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5x + x2 = -8 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -8 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5x + x2 = -1.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -1.75 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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