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Simplifying 24a2 = 16a + -44 Reorder the terms: 24a2 = -44 + 16a Solving 24a2 = -44 + 16a Solving for variable 'a'. Reorder the terms: 44 + -16a + 24a2 = -44 + 16a + 44 + -16a Reorder the terms: 44 + -16a + 24a2 = -44 + 44 + 16a + -16a Combine like terms: -44 + 44 = 0 44 + -16a + 24a2 = 0 + 16a + -16a 44 + -16a + 24a2 = 16a + -16a Combine like terms: 16a + -16a = 0 44 + -16a + 24a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -4a + 6a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -4a + 6a2)' equal to zero and attempt to solve: Simplifying 11 + -4a + 6a2 = 0 Solving 11 + -4a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -0.6666666667a + a2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -0.6666666667a + -1.833333333 + a2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -0.6666666667a + a2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -0.6666666667a + a2 = 0 + -1.833333333 -0.6666666667a + a2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -0.6666666667a + a2 = -1.833333333 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 = -1.833333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667a + a2 = -1.833333333 + 0.1111111112 Combine like terms: -1.833333333 + 0.1111111112 = -1.7222222218 0.1111111112 + -0.6666666667a + a2 = -1.7222222218 Factor a perfect square on the left side: (a + -0.3333333334)(a + -0.3333333334) = -1.7222222218 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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