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Simplifying a2 + -34a + 96 = 0 Reorder the terms: 96 + -34a + a2 = 0 Solving 96 + -34a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -34a + -96 + a2 = 0 + -96 Reorder the terms: 96 + -96 + -34a + a2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -34a + a2 = 0 + -96 -34a + a2 = 0 + -96 Combine like terms: 0 + -96 = -96 -34a + a2 = -96 The a term is -34a. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34a + 289 + a2 = -96 + 289 Reorder the terms: 289 + -34a + a2 = -96 + 289 Combine like terms: -96 + 289 = 193 289 + -34a + a2 = 193 Factor a perfect square on the left side: (a + -17)(a + -17) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (a + -17) equal to 13.892443989 and -13.892443989.Subproblem 1
a + -17 = 13.892443989 Simplifying a + -17 = 13.892443989 Reorder the terms: -17 + a = 13.892443989 Solving -17 + a = 13.892443989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + a = 13.892443989 + 17 Combine like terms: -17 + 17 = 0 0 + a = 13.892443989 + 17 a = 13.892443989 + 17 Combine like terms: 13.892443989 + 17 = 30.892443989 a = 30.892443989 Simplifying a = 30.892443989Subproblem 2
a + -17 = -13.892443989 Simplifying a + -17 = -13.892443989 Reorder the terms: -17 + a = -13.892443989 Solving -17 + a = -13.892443989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + a = -13.892443989 + 17 Combine like terms: -17 + 17 = 0 0 + a = -13.892443989 + 17 a = -13.892443989 + 17 Combine like terms: -13.892443989 + 17 = 3.107556011 a = 3.107556011 Simplifying a = 3.107556011Solution
The solution to the problem is based on the solutions from the subproblems. a = {30.892443989, 3.107556011}
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