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Simplifying 17 + -17a = -2a2 Solving 17 + -17a = -2a2 Solving for variable 'a'. Combine like terms: -2a2 + 2a2 = 0 17 + -17a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -8.5a + a2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -8.5a + -8.5 + a2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -8.5a + a2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -8.5a + a2 = 0 + -8.5 -8.5a + a2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -8.5a + a2 = -8.5 The a term is -8.5a. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5a + 18.0625 + a2 = -8.5 + 18.0625 Reorder the terms: 18.0625 + -8.5a + a2 = -8.5 + 18.0625 Combine like terms: -8.5 + 18.0625 = 9.5625 18.0625 + -8.5a + a2 = 9.5625 Factor a perfect square on the left side: (a + -4.25)(a + -4.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (a + -4.25) equal to 3.092329219 and -3.092329219.Subproblem 1
a + -4.25 = 3.092329219 Simplifying a + -4.25 = 3.092329219 Reorder the terms: -4.25 + a = 3.092329219 Solving -4.25 + a = 3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + a = 3.092329219 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + a = 3.092329219 + 4.25 a = 3.092329219 + 4.25 Combine like terms: 3.092329219 + 4.25 = 7.342329219 a = 7.342329219 Simplifying a = 7.342329219Subproblem 2
a + -4.25 = -3.092329219 Simplifying a + -4.25 = -3.092329219 Reorder the terms: -4.25 + a = -3.092329219 Solving -4.25 + a = -3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + a = -3.092329219 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + a = -3.092329219 + 4.25 a = -3.092329219 + 4.25 Combine like terms: -3.092329219 + 4.25 = 1.157670781 a = 1.157670781 Simplifying a = 1.157670781Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.342329219, 1.157670781}
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