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Simplifying -6a(a + -3) + -8(7 + 4a) = -38 Reorder the terms: -6a(-3 + a) + -8(7 + 4a) = -38 (-3 * -6a + a * -6a) + -8(7 + 4a) = -38 (18a + -6a2) + -8(7 + 4a) = -38 18a + -6a2 + (7 * -8 + 4a * -8) = -38 18a + -6a2 + (-56 + -32a) = -38 Reorder the terms: -56 + 18a + -32a + -6a2 = -38 Combine like terms: 18a + -32a = -14a -56 + -14a + -6a2 = -38 Solving -56 + -14a + -6a2 = -38 Solving for variable 'a'. Reorder the terms: -56 + 38 + -14a + -6a2 = -38 + 38 Combine like terms: -56 + 38 = -18 -18 + -14a + -6a2 = -38 + 38 Combine like terms: -38 + 38 = 0 -18 + -14a + -6a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 7a + 3a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(9 + 7a + 3a2)' equal to zero and attempt to solve: Simplifying 9 + 7a + 3a2 = 0 Solving 9 + 7a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 2.333333333a + a2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.333333333a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + 2.333333333a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.333333333a + a2 = 0 + -3 2.333333333a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.333333333a + a2 = -3 The a term is 2.333333333a. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333a + 1.361111112 + a2 = -3 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333a + a2 = -3 + 1.361111112 Combine like terms: -3 + 1.361111112 = -1.638888888 1.361111112 + 2.333333333a + a2 = -1.638888888 Factor a perfect square on the left side: (a + 1.166666667)(a + 1.166666667) = -1.638888888 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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