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Simplifying (5a + -3a2) + -1(-6a + -6) = 0 Remove parenthesis around (5a + -3a2) 5a + -3a2 + -1(-6a + -6) = 0 Reorder the terms: 5a + -3a2 + -1(-6 + -6a) = 0 5a + -3a2 + (-6 * -1 + -6a * -1) = 0 5a + -3a2 + (6 + 6a) = 0 Reorder the terms: 6 + 5a + 6a + -3a2 = 0 Combine like terms: 5a + 6a = 11a 6 + 11a + -3a2 = 0 Solving 6 + 11a + -3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + -3.666666667a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.666666667a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -3.666666667a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.666666667a + a2 = 0 + 2 -3.666666667a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.666666667a + a2 = 2 The a term is -3.666666667a. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667a + 3.361111114 + a2 = 2 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667a + a2 = 2 + 3.361111114 Combine like terms: 2 + 3.361111114 = 5.361111114 3.361111114 + -3.666666667a + a2 = 5.361111114 Factor a perfect square on the left side: (a + -1.833333334)(a + -1.833333334) = 5.361111114 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (a + -1.833333334) equal to 2.315407332 and -2.315407332.Subproblem 1
a + -1.833333334 = 2.315407332 Simplifying a + -1.833333334 = 2.315407332 Reorder the terms: -1.833333334 + a = 2.315407332 Solving -1.833333334 + a = 2.315407332 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + a = 2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + a = 2.315407332 + 1.833333334 a = 2.315407332 + 1.833333334 Combine like terms: 2.315407332 + 1.833333334 = 4.148740666 a = 4.148740666 Simplifying a = 4.148740666Subproblem 2
a + -1.833333334 = -2.315407332 Simplifying a + -1.833333334 = -2.315407332 Reorder the terms: -1.833333334 + a = -2.315407332 Solving -1.833333334 + a = -2.315407332 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + a = -2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + a = -2.315407332 + 1.833333334 a = -2.315407332 + 1.833333334 Combine like terms: -2.315407332 + 1.833333334 = -0.482073998 a = -0.482073998 Simplifying a = -0.482073998Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.148740666, -0.482073998}
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