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Simplifying 17a2 + 3a + -2 = 0 Reorder the terms: -2 + 3a + 17a2 = 0 Solving -2 + 3a + 17a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1176470588 + 0.1764705882a + a2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + 0.1764705882a + 0.1176470588 + a2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + 0.1764705882a + a2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + 0.1764705882a + a2 = 0 + 0.1176470588 0.1764705882a + a2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 0.1764705882a + a2 = 0.1176470588 The a term is 0.1764705882a. Take half its coefficient (0.0882352941). Square it (0.007785467125) and add it to both sides. Add '0.007785467125' to each side of the equation. 0.1764705882a + 0.007785467125 + a2 = 0.1176470588 + 0.007785467125 Reorder the terms: 0.007785467125 + 0.1764705882a + a2 = 0.1176470588 + 0.007785467125 Combine like terms: 0.1176470588 + 0.007785467125 = 0.125432525925 0.007785467125 + 0.1764705882a + a2 = 0.125432525925 Factor a perfect square on the left side: (a + 0.0882352941)(a + 0.0882352941) = 0.125432525925 Calculate the square root of the right side: 0.354164546 Break this problem into two subproblems by setting (a + 0.0882352941) equal to 0.354164546 and -0.354164546.Subproblem 1
a + 0.0882352941 = 0.354164546 Simplifying a + 0.0882352941 = 0.354164546 Reorder the terms: 0.0882352941 + a = 0.354164546 Solving 0.0882352941 + a = 0.354164546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + a = 0.354164546 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + a = 0.354164546 + -0.0882352941 a = 0.354164546 + -0.0882352941 Combine like terms: 0.354164546 + -0.0882352941 = 0.2659292519 a = 0.2659292519 Simplifying a = 0.2659292519Subproblem 2
a + 0.0882352941 = -0.354164546 Simplifying a + 0.0882352941 = -0.354164546 Reorder the terms: 0.0882352941 + a = -0.354164546 Solving 0.0882352941 + a = -0.354164546 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + a = -0.354164546 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + a = -0.354164546 + -0.0882352941 a = -0.354164546 + -0.0882352941 Combine like terms: -0.354164546 + -0.0882352941 = -0.4423998401 a = -0.4423998401 Simplifying a = -0.4423998401Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.2659292519, -0.4423998401}
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