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Simplifying -3x2 + 27x + -108 = 0 Reorder the terms: -108 + 27x + -3x2 = 0 Solving -108 + 27x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + 9x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-36 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying -36 + 9x + -1x2 = 0 Solving -36 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -9x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -9x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -9x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -9x + x2 = 0 + -36 -9x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -9x + x2 = -36 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -36 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -36 + 20.25 Combine like terms: -36 + 20.25 = -15.75 20.25 + -9x + x2 = -15.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = -15.75 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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