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Simplifying a2 + 9a + -17 = 0 Reorder the terms: -17 + 9a + a2 = 0 Solving -17 + 9a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 9a + 17 + a2 = 0 + 17 Reorder the terms: -17 + 17 + 9a + a2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 9a + a2 = 0 + 17 9a + a2 = 0 + 17 Combine like terms: 0 + 17 = 17 9a + a2 = 17 The a term is 9a. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9a + 20.25 + a2 = 17 + 20.25 Reorder the terms: 20.25 + 9a + a2 = 17 + 20.25 Combine like terms: 17 + 20.25 = 37.25 20.25 + 9a + a2 = 37.25 Factor a perfect square on the left side: (a + 4.5)(a + 4.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (a + 4.5) equal to 6.103277808 and -6.103277808.Subproblem 1
a + 4.5 = 6.103277808 Simplifying a + 4.5 = 6.103277808 Reorder the terms: 4.5 + a = 6.103277808 Solving 4.5 + a = 6.103277808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = 6.103277808 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = 6.103277808 + -4.5 a = 6.103277808 + -4.5 Combine like terms: 6.103277808 + -4.5 = 1.603277808 a = 1.603277808 Simplifying a = 1.603277808Subproblem 2
a + 4.5 = -6.103277808 Simplifying a + 4.5 = -6.103277808 Reorder the terms: 4.5 + a = -6.103277808 Solving 4.5 + a = -6.103277808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + a = -6.103277808 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + a = -6.103277808 + -4.5 a = -6.103277808 + -4.5 Combine like terms: -6.103277808 + -4.5 = -10.603277808 a = -10.603277808 Simplifying a = -10.603277808Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.603277808, -10.603277808}
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