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Simplifying -3a2 + -4a(2a + 3) + 7(a + -8) = 0 Reorder the terms: -3a2 + -4a(3 + 2a) + 7(a + -8) = 0 -3a2 + (3 * -4a + 2a * -4a) + 7(a + -8) = 0 -3a2 + (-12a + -8a2) + 7(a + -8) = 0 Reorder the terms: -3a2 + -12a + -8a2 + 7(-8 + a) = 0 -3a2 + -12a + -8a2 + (-8 * 7 + a * 7) = 0 -3a2 + -12a + -8a2 + (-56 + 7a) = 0 Reorder the terms: -56 + -12a + 7a + -3a2 + -8a2 = 0 Combine like terms: -12a + 7a = -5a -56 + -5a + -3a2 + -8a2 = 0 Combine like terms: -3a2 + -8a2 = -11a2 -56 + -5a + -11a2 = 0 Solving -56 + -5a + -11a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(56 + 5a + 11a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(56 + 5a + 11a2)' equal to zero and attempt to solve: Simplifying 56 + 5a + 11a2 = 0 Solving 56 + 5a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 5.090909091 + 0.4545454545a + a2 = 0 Move the constant term to the right: Add '-5.090909091' to each side of the equation. 5.090909091 + 0.4545454545a + -5.090909091 + a2 = 0 + -5.090909091 Reorder the terms: 5.090909091 + -5.090909091 + 0.4545454545a + a2 = 0 + -5.090909091 Combine like terms: 5.090909091 + -5.090909091 = 0.000000000 0.000000000 + 0.4545454545a + a2 = 0 + -5.090909091 0.4545454545a + a2 = 0 + -5.090909091 Combine like terms: 0 + -5.090909091 = -5.090909091 0.4545454545a + a2 = -5.090909091 The a term is 0.4545454545a. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545a + 0.05165289257 + a2 = -5.090909091 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545a + a2 = -5.090909091 + 0.05165289257 Combine like terms: -5.090909091 + 0.05165289257 = -5.03925619843 0.05165289257 + 0.4545454545a + a2 = -5.03925619843 Factor a perfect square on the left side: (a + 0.2272727273)(a + 0.2272727273) = -5.03925619843 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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