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Simplifying -8x4 + 24x3 + -88x2 = 0 Reorder the terms: -88x2 + 24x3 + -8x4 = 0 Solving -88x2 + 24x3 + -8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x2'. 8x2(-11 + 3x + -1x2) = 0 Ignore the factor 8.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 '(-11 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -11 + 3x + -1x2 = 0 Solving -11 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -3x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -3x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -3x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3x + x2 = 0 + -11 -3x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -3x + x2 = -11 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 = -11 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -11 + 2.25 Combine like terms: -11 + 2.25 = -8.75 2.25 + -3x + x2 = -8.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -8.75 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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