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Simplifying 2a2 + -13a + 17 = 0 Reorder the terms: 17 + -13a + 2a2 = 0 Solving 17 + -13a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -6.5a + a2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -6.5a + -8.5 + a2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -6.5a + a2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -6.5a + a2 = 0 + -8.5 -6.5a + a2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -6.5a + a2 = -8.5 The a term is -6.5a. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5a + 10.5625 + a2 = -8.5 + 10.5625 Reorder the terms: 10.5625 + -6.5a + a2 = -8.5 + 10.5625 Combine like terms: -8.5 + 10.5625 = 2.0625 10.5625 + -6.5a + a2 = 2.0625 Factor a perfect square on the left side: (a + -3.25)(a + -3.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (a + -3.25) equal to 1.436140662 and -1.436140662.Subproblem 1
a + -3.25 = 1.436140662 Simplifying a + -3.25 = 1.436140662 Reorder the terms: -3.25 + a = 1.436140662 Solving -3.25 + a = 1.436140662 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = 1.436140662 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = 1.436140662 + 3.25 a = 1.436140662 + 3.25 Combine like terms: 1.436140662 + 3.25 = 4.686140662 a = 4.686140662 Simplifying a = 4.686140662Subproblem 2
a + -3.25 = -1.436140662 Simplifying a + -3.25 = -1.436140662 Reorder the terms: -3.25 + a = -1.436140662 Solving -3.25 + a = -1.436140662 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = -1.436140662 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = -1.436140662 + 3.25 a = -1.436140662 + 3.25 Combine like terms: -1.436140662 + 3.25 = 1.813859338 a = 1.813859338 Simplifying a = 1.813859338Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.686140662, 1.813859338}
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