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Simplifying 16a2 + 13a + -35 = 0 Reorder the terms: -35 + 13a + 16a2 = 0 Solving -35 + 13a + 16a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + 0.8125a + a2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + 0.8125a + 2.1875 + a2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + 0.8125a + a2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + 0.8125a + a2 = 0 + 2.1875 0.8125a + a2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 0.8125a + a2 = 2.1875 The a term is 0.8125a. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125a + 0.1650390625 + a2 = 2.1875 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125a + a2 = 2.1875 + 0.1650390625 Combine like terms: 2.1875 + 0.1650390625 = 2.3525390625 0.1650390625 + 0.8125a + a2 = 2.3525390625 Factor a perfect square on the left side: (a + 0.40625)(a + 0.40625) = 2.3525390625 Calculate the square root of the right side: 1.533798899 Break this problem into two subproblems by setting (a + 0.40625) equal to 1.533798899 and -1.533798899.Subproblem 1
a + 0.40625 = 1.533798899 Simplifying a + 0.40625 = 1.533798899 Reorder the terms: 0.40625 + a = 1.533798899 Solving 0.40625 + a = 1.533798899 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + a = 1.533798899 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + a = 1.533798899 + -0.40625 a = 1.533798899 + -0.40625 Combine like terms: 1.533798899 + -0.40625 = 1.127548899 a = 1.127548899 Simplifying a = 1.127548899Subproblem 2
a + 0.40625 = -1.533798899 Simplifying a + 0.40625 = -1.533798899 Reorder the terms: 0.40625 + a = -1.533798899 Solving 0.40625 + a = -1.533798899 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + a = -1.533798899 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + a = -1.533798899 + -0.40625 a = -1.533798899 + -0.40625 Combine like terms: -1.533798899 + -0.40625 = -1.940048899 a = -1.940048899 Simplifying a = -1.940048899Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.127548899, -1.940048899}
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