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Simplifying 3a2 + 24a + -169 = 0 Reorder the terms: -169 + 24a + 3a2 = 0 Solving -169 + 24a + 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'. -56.33333333 + 8a + a2 = 0 Move the constant term to the right: Add '56.33333333' to each side of the equation. -56.33333333 + 8a + 56.33333333 + a2 = 0 + 56.33333333 Reorder the terms: -56.33333333 + 56.33333333 + 8a + a2 = 0 + 56.33333333 Combine like terms: -56.33333333 + 56.33333333 = 0.00000000 0.00000000 + 8a + a2 = 0 + 56.33333333 8a + a2 = 0 + 56.33333333 Combine like terms: 0 + 56.33333333 = 56.33333333 8a + a2 = 56.33333333 The a term is 8a. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8a + 16 + a2 = 56.33333333 + 16 Reorder the terms: 16 + 8a + a2 = 56.33333333 + 16 Combine like terms: 56.33333333 + 16 = 72.33333333 16 + 8a + a2 = 72.33333333 Factor a perfect square on the left side: (a + 4)(a + 4) = 72.33333333 Calculate the square root of the right side: 8.504900548 Break this problem into two subproblems by setting (a + 4) equal to 8.504900548 and -8.504900548.Subproblem 1
a + 4 = 8.504900548 Simplifying a + 4 = 8.504900548 Reorder the terms: 4 + a = 8.504900548 Solving 4 + a = 8.504900548 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 8.504900548 + -4 Combine like terms: 4 + -4 = 0 0 + a = 8.504900548 + -4 a = 8.504900548 + -4 Combine like terms: 8.504900548 + -4 = 4.504900548 a = 4.504900548 Simplifying a = 4.504900548Subproblem 2
a + 4 = -8.504900548 Simplifying a + 4 = -8.504900548 Reorder the terms: 4 + a = -8.504900548 Solving 4 + a = -8.504900548 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -8.504900548 + -4 Combine like terms: 4 + -4 = 0 0 + a = -8.504900548 + -4 a = -8.504900548 + -4 Combine like terms: -8.504900548 + -4 = -12.504900548 a = -12.504900548 Simplifying a = -12.504900548Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.504900548, -12.504900548}
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