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Simplifying 3a(2a + -5) = 13 + -2(a + 12) Reorder the terms: 3a(-5 + 2a) = 13 + -2(a + 12) (-5 * 3a + 2a * 3a) = 13 + -2(a + 12) (-15a + 6a2) = 13 + -2(a + 12) Reorder the terms: -15a + 6a2 = 13 + -2(12 + a) -15a + 6a2 = 13 + (12 * -2 + a * -2) -15a + 6a2 = 13 + (-24 + -2a) Combine like terms: 13 + -24 = -11 -15a + 6a2 = -11 + -2a Solving -15a + 6a2 = -11 + -2a Solving for variable 'a'. Reorder the terms: 11 + -15a + 2a + 6a2 = -11 + -2a + 11 + 2a Combine like terms: -15a + 2a = -13a 11 + -13a + 6a2 = -11 + -2a + 11 + 2a Reorder the terms: 11 + -13a + 6a2 = -11 + 11 + -2a + 2a Combine like terms: -11 + 11 = 0 11 + -13a + 6a2 = 0 + -2a + 2a 11 + -13a + 6a2 = -2a + 2a Combine like terms: -2a + 2a = 0 11 + -13a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -2.166666667a + a2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -2.166666667a + -1.833333333 + a2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -2.166666667a + a2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -2.166666667a + a2 = 0 + -1.833333333 -2.166666667a + a2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -2.166666667a + a2 = -1.833333333 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 = -1.833333333 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667a + a2 = -1.833333333 + 1.173611113 Combine like terms: -1.833333333 + 1.173611113 = -0.65972222 1.173611113 + -2.166666667a + a2 = -0.65972222 Factor a perfect square on the left side: (a + -1.083333334)(a + -1.083333334) = -0.65972222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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