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Simplifying 9a2 = 6a + -24 Reorder the terms: 9a2 = -24 + 6a Solving 9a2 = -24 + 6a Solving for variable 'a'. Reorder the terms: 24 + -6a + 9a2 = -24 + 6a + 24 + -6a Reorder the terms: 24 + -6a + 9a2 = -24 + 24 + 6a + -6a Combine like terms: -24 + 24 = 0 24 + -6a + 9a2 = 0 + 6a + -6a 24 + -6a + 9a2 = 6a + -6a Combine like terms: 6a + -6a = 0 24 + -6a + 9a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -2a + 3a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -2a + 3a2)' equal to zero and attempt to solve: Simplifying 8 + -2a + 3a2 = 0 Solving 8 + -2a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -0.6666666667a + a2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -0.6666666667a + -2.666666667 + a2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -0.6666666667a + a2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -0.6666666667a + a2 = 0 + -2.666666667 -0.6666666667a + a2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -0.6666666667a + a2 = -2.666666667 The a term is -0.6666666667a. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667a + 0.1111111112 + a2 = -2.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667a + a2 = -2.666666667 + 0.1111111112 Combine like terms: -2.666666667 + 0.1111111112 = -2.5555555558 0.1111111112 + -0.6666666667a + a2 = -2.5555555558 Factor a perfect square on the left side: (a + -0.3333333334)(a + -0.3333333334) = -2.5555555558 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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