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Simplifying -2(a2 + -9a + 54) = 0 Reorder the terms: -2(54 + -9a + a2) = 0 (54 * -2 + -9a * -2 + a2 * -2) = 0 (-108 + 18a + -2a2) = 0 Solving -108 + 18a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 9a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + 9a + -1a2)' equal to zero and attempt to solve: Simplifying -54 + 9a + -1a2 = 0 Solving -54 + 9a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 54 + -9a + a2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -9a + -54 + a2 = 0 + -54 Reorder the terms: 54 + -54 + -9a + a2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -9a + a2 = 0 + -54 -9a + a2 = 0 + -54 Combine like terms: 0 + -54 = -54 -9a + a2 = -54 The a term is -9a. 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. -9a + 20.25 + a2 = -54 + 20.25 Reorder the terms: 20.25 + -9a + a2 = -54 + 20.25 Combine like terms: -54 + 20.25 = -33.75 20.25 + -9a + a2 = -33.75 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = -33.75 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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