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Simplifying a2 + 11a + 18 = 1 Reorder the terms: 18 + 11a + a2 = 1 Solving 18 + 11a + a2 = 1 Solving for variable 'a'. Reorder the terms: 18 + -1 + 11a + a2 = 1 + -1 Combine like terms: 18 + -1 = 17 17 + 11a + a2 = 1 + -1 Combine like terms: 1 + -1 = 0 17 + 11a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 11a + -17 + a2 = 0 + -17 Reorder the terms: 17 + -17 + 11a + a2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 11a + a2 = 0 + -17 11a + a2 = 0 + -17 Combine like terms: 0 + -17 = -17 11a + a2 = -17 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = -17 + 30.25 Reorder the terms: 30.25 + 11a + a2 = -17 + 30.25 Combine like terms: -17 + 30.25 = 13.25 30.25 + 11a + a2 = 13.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (a + 5.5) equal to 3.640054945 and -3.640054945.Subproblem 1
a + 5.5 = 3.640054945 Simplifying a + 5.5 = 3.640054945 Reorder the terms: 5.5 + a = 3.640054945 Solving 5.5 + a = 3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 3.640054945 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 3.640054945 + -5.5 a = 3.640054945 + -5.5 Combine like terms: 3.640054945 + -5.5 = -1.859945055 a = -1.859945055 Simplifying a = -1.859945055Subproblem 2
a + 5.5 = -3.640054945 Simplifying a + 5.5 = -3.640054945 Reorder the terms: 5.5 + a = -3.640054945 Solving 5.5 + a = -3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -3.640054945 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -3.640054945 + -5.5 a = -3.640054945 + -5.5 Combine like terms: -3.640054945 + -5.5 = -9.140054945 a = -9.140054945 Simplifying a = -9.140054945Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.859945055, -9.140054945}
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