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Simplifying a2 + a + -1483 = 0 Reorder the terms: -1483 + a + a2 = 0 Solving -1483 + a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '1483' to each side of the equation. -1483 + a + 1483 + a2 = 0 + 1483 Reorder the terms: -1483 + 1483 + a + a2 = 0 + 1483 Combine like terms: -1483 + 1483 = 0 0 + a + a2 = 0 + 1483 a + a2 = 0 + 1483 Combine like terms: 0 + 1483 = 1483 a + a2 = 1483 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a + 0.25 + a2 = 1483 + 0.25 Reorder the terms: 0.25 + a + a2 = 1483 + 0.25 Combine like terms: 1483 + 0.25 = 1483.25 0.25 + a + a2 = 1483.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 1483.25 Calculate the square root of the right side: 38.512984823 Break this problem into two subproblems by setting (a + 0.5) equal to 38.512984823 and -38.512984823.Subproblem 1
a + 0.5 = 38.512984823 Simplifying a + 0.5 = 38.512984823 Reorder the terms: 0.5 + a = 38.512984823 Solving 0.5 + a = 38.512984823 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 38.512984823 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 38.512984823 + -0.5 a = 38.512984823 + -0.5 Combine like terms: 38.512984823 + -0.5 = 38.012984823 a = 38.012984823 Simplifying a = 38.012984823Subproblem 2
a + 0.5 = -38.512984823 Simplifying a + 0.5 = -38.512984823 Reorder the terms: 0.5 + a = -38.512984823 Solving 0.5 + a = -38.512984823 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -38.512984823 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -38.512984823 + -0.5 a = -38.512984823 + -0.5 Combine like terms: -38.512984823 + -0.5 = -39.012984823 a = -39.012984823 Simplifying a = -39.012984823Solution
The solution to the problem is based on the solutions from the subproblems. a = {38.012984823, -39.012984823}
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