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Simplifying 3(a + 5) + -2a(8 + -3a) = 0 Reorder the terms: 3(5 + a) + -2a(8 + -3a) = 0 (5 * 3 + a * 3) + -2a(8 + -3a) = 0 (15 + 3a) + -2a(8 + -3a) = 0 15 + 3a + (8 * -2a + -3a * -2a) = 0 15 + 3a + (-16a + 6a2) = 0 Combine like terms: 3a + -16a = -13a 15 + -13a + 6a2 = 0 Solving 15 + -13a + 6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + -2.166666667a + a2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2.166666667a + -2.5 + a2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2.166666667a + a2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.166666667a + a2 = 0 + -2.5 -2.166666667a + a2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2.166666667a + a2 = -2.5 The a term is -2.166666667a. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667a + 1.173611113 + a2 = -2.5 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667a + a2 = -2.5 + 1.173611113 Combine like terms: -2.5 + 1.173611113 = -1.326388887 1.173611113 + -2.166666667a + a2 = -1.326388887 Factor a perfect square on the left side: (a + -1.083333334)(a + -1.083333334) = -1.326388887 Can't calculate square root of the right side. The solution to this equation could not be determined.
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