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Simplifying a2 + 6a + -63 = 0 Reorder the terms: -63 + 6a + a2 = 0 Solving -63 + 6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 6a + 63 + a2 = 0 + 63 Reorder the terms: -63 + 63 + 6a + a2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 6a + a2 = 0 + 63 6a + a2 = 0 + 63 Combine like terms: 0 + 63 = 63 6a + a2 = 63 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 63 + 9 Reorder the terms: 9 + 6a + a2 = 63 + 9 Combine like terms: 63 + 9 = 72 9 + 6a + a2 = 72 Factor a perfect square on the left side: (a + 3)(a + 3) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (a + 3) equal to 8.485281374 and -8.485281374.Subproblem 1
a + 3 = 8.485281374 Simplifying a + 3 = 8.485281374 Reorder the terms: 3 + a = 8.485281374 Solving 3 + a = 8.485281374 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + a = 8.485281374 + -3 a = 8.485281374 + -3 Combine like terms: 8.485281374 + -3 = 5.485281374 a = 5.485281374 Simplifying a = 5.485281374Subproblem 2
a + 3 = -8.485281374 Simplifying a + 3 = -8.485281374 Reorder the terms: 3 + a = -8.485281374 Solving 3 + a = -8.485281374 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + a = -8.485281374 + -3 a = -8.485281374 + -3 Combine like terms: -8.485281374 + -3 = -11.485281374 a = -11.485281374 Simplifying a = -11.485281374Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.485281374, -11.485281374}
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