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Simplifying 0 = 3x2 + -9x + 24 Reorder the terms: 0 = 24 + -9x + 3x2 Solving 0 = 24 + -9x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 9x + -3x2 = 24 + -9x + 3x2 + -24 + 9x + -3x2 Reorder the terms: -24 + 9x + -3x2 = 24 + -24 + -9x + 9x + 3x2 + -3x2 Combine like terms: 24 + -24 = 0 -24 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2 -24 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2 Combine like terms: -9x + 9x = 0 -24 + 9x + -3x2 = 0 + 3x2 + -3x2 -24 + 9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -24 + 9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 3x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + -1x2 = 0 Solving -8 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -3x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -3x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -3x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x + x2 = 0 + -8 -3x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3x + x2 = -8 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 = -8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -8 + 2.25 Combine like terms: -8 + 2.25 = -5.75 2.25 + -3x + x2 = -5.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -5.75 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. The solution to this equation could not be determined.
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