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Simplifying a2 + -2a + -49 = 3 Reorder the terms: -49 + -2a + a2 = 3 Solving -49 + -2a + a2 = 3 Solving for variable 'a'. Reorder the terms: -49 + -3 + -2a + a2 = 3 + -3 Combine like terms: -49 + -3 = -52 -52 + -2a + a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -52 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -2a + 52 + a2 = 0 + 52 Reorder the terms: -52 + 52 + -2a + a2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -2a + a2 = 0 + 52 -2a + a2 = 0 + 52 Combine like terms: 0 + 52 = 52 -2a + a2 = 52 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 52 + 1 Reorder the terms: 1 + -2a + a2 = 52 + 1 Combine like terms: 52 + 1 = 53 1 + -2a + a2 = 53 Factor a perfect square on the left side: (a + -1)(a + -1) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (a + -1) equal to 7.280109889 and -7.280109889.Subproblem 1
a + -1 = 7.280109889 Simplifying a + -1 = 7.280109889 Reorder the terms: -1 + a = 7.280109889 Solving -1 + a = 7.280109889 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + a = 7.280109889 + 1 a = 7.280109889 + 1 Combine like terms: 7.280109889 + 1 = 8.280109889 a = 8.280109889 Simplifying a = 8.280109889Subproblem 2
a + -1 = -7.280109889 Simplifying a + -1 = -7.280109889 Reorder the terms: -1 + a = -7.280109889 Solving -1 + a = -7.280109889 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + a = -7.280109889 + 1 a = -7.280109889 + 1 Combine like terms: -7.280109889 + 1 = -6.280109889 a = -6.280109889 Simplifying a = -6.280109889Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.280109889, -6.280109889}
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