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Simplifying 9a(-3a2 + a + -5) = 0 Reorder the terms: 9a(-5 + a + -3a2) = 0 (-5 * 9a + a * 9a + -3a2 * 9a) = 0 (-45a + 9a2 + -27a3) = 0 Solving -45a + 9a2 + -27a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9a'. 9a(-5 + a + -3a2) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-5 + a + -3a2)' equal to zero and attempt to solve: Simplifying -5 + a + -3a2 = 0 Solving -5 + a + -3a2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -0.3333333333a + a2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -0.3333333333a + -1.666666667 + a2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -0.3333333333a + a2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -0.3333333333a + a2 = 0 + -1.666666667 -0.3333333333a + a2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -0.3333333333a + a2 = -1.666666667 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.3333333333a + 0.25 + a2 = -1.666666667 + 0.25 Reorder the terms: 0.25 + -0.3333333333a + a2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 0.25 + -0.3333333333a + a2 = -1.416666667 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -1.416666667 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
a = {0}
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