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Simplifying a2 + 3a + -63 = 0 Reorder the terms: -63 + 3a + a2 = 0 Solving -63 + 3a + 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 + 3a + 63 + a2 = 0 + 63 Reorder the terms: -63 + 63 + 3a + a2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 3a + a2 = 0 + 63 3a + a2 = 0 + 63 Combine like terms: 0 + 63 = 63 3a + a2 = 63 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 63 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 63 + 2.25 Combine like terms: 63 + 2.25 = 65.25 2.25 + 3a + a2 = 65.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (a + 1.5) equal to 8.077747211 and -8.077747211.Subproblem 1
a + 1.5 = 8.077747211 Simplifying a + 1.5 = 8.077747211 Reorder the terms: 1.5 + a = 8.077747211 Solving 1.5 + a = 8.077747211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 8.077747211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 8.077747211 + -1.5 a = 8.077747211 + -1.5 Combine like terms: 8.077747211 + -1.5 = 6.577747211 a = 6.577747211 Simplifying a = 6.577747211Subproblem 2
a + 1.5 = -8.077747211 Simplifying a + 1.5 = -8.077747211 Reorder the terms: 1.5 + a = -8.077747211 Solving 1.5 + a = -8.077747211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -8.077747211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -8.077747211 + -1.5 a = -8.077747211 + -1.5 Combine like terms: -8.077747211 + -1.5 = -9.577747211 a = -9.577747211 Simplifying a = -9.577747211Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.577747211, -9.577747211}
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