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Simplifying (5a2 + -3a + 8) + (-4a2 + -1) + (15a + 11) = 0 Reorder the terms: (8 + -3a + 5a2) + (-4a2 + -1) + (15a + 11) = 0 Remove parenthesis around (8 + -3a + 5a2) 8 + -3a + 5a2 + (-4a2 + -1) + (15a + 11) = 0 Reorder the terms: 8 + -3a + 5a2 + (-1 + -4a2) + (15a + 11) = 0 Remove parenthesis around (-1 + -4a2) 8 + -3a + 5a2 + -1 + -4a2 + (15a + 11) = 0 Reorder the terms: 8 + -3a + 5a2 + -1 + -4a2 + (11 + 15a) = 0 Remove parenthesis around (11 + 15a) 8 + -3a + 5a2 + -1 + -4a2 + 11 + 15a = 0 Reorder the terms: 8 + -1 + 11 + -3a + 15a + 5a2 + -4a2 = 0 Combine like terms: 8 + -1 = 7 7 + 11 + -3a + 15a + 5a2 + -4a2 = 0 Combine like terms: 7 + 11 = 18 18 + -3a + 15a + 5a2 + -4a2 = 0 Combine like terms: -3a + 15a = 12a 18 + 12a + 5a2 + -4a2 = 0 Combine like terms: 5a2 + -4a2 = 1a2 18 + 12a + 1a2 = 0 Solving 18 + 12a + 1a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 12a + -18 + a2 = 0 + -18 Reorder the terms: 18 + -18 + 12a + a2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12a + a2 = 0 + -18 12a + a2 = 0 + -18 Combine like terms: 0 + -18 = -18 12a + a2 = -18 The a term is 12a. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12a + 36 + a2 = -18 + 36 Reorder the terms: 36 + 12a + a2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + 12a + a2 = 18 Factor a perfect square on the left side: (a + 6)(a + 6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (a + 6) equal to 4.242640687 and -4.242640687.Subproblem 1
a + 6 = 4.242640687 Simplifying a + 6 = 4.242640687 Reorder the terms: 6 + a = 4.242640687 Solving 6 + a = 4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + a = 4.242640687 + -6 a = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 a = -1.757359313 Simplifying a = -1.757359313Subproblem 2
a + 6 = -4.242640687 Simplifying a + 6 = -4.242640687 Reorder the terms: 6 + a = -4.242640687 Solving 6 + a = -4.242640687 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + a = -4.242640687 + -6 a = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 a = -10.242640687 Simplifying a = -10.242640687Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.757359313, -10.242640687}
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