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Simplifying 16n2 + -4n + -15 = 0 Reorder the terms: -15 + -4n + 16n2 = 0 Solving -15 + -4n + 16n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -0.25n + n2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.25n + 0.9375 + n2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.25n + n2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.25n + n2 = 0 + 0.9375 -0.25n + n2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.25n + n2 = 0.9375 The n term is -0.25n. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25n + 0.015625 + n2 = 0.9375 + 0.015625 Reorder the terms: 0.015625 + -0.25n + n2 = 0.9375 + 0.015625 Combine like terms: 0.9375 + 0.015625 = 0.953125 0.015625 + -0.25n + n2 = 0.953125 Factor a perfect square on the left side: (n + -0.125)(n + -0.125) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (n + -0.125) equal to 0.976281209 and -0.976281209.Subproblem 1
n + -0.125 = 0.976281209 Simplifying n + -0.125 = 0.976281209 Reorder the terms: -0.125 + n = 0.976281209 Solving -0.125 + n = 0.976281209 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = 0.976281209 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = 0.976281209 + 0.125 n = 0.976281209 + 0.125 Combine like terms: 0.976281209 + 0.125 = 1.101281209 n = 1.101281209 Simplifying n = 1.101281209Subproblem 2
n + -0.125 = -0.976281209 Simplifying n + -0.125 = -0.976281209 Reorder the terms: -0.125 + n = -0.976281209 Solving -0.125 + n = -0.976281209 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = -0.976281209 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = -0.976281209 + 0.125 n = -0.976281209 + 0.125 Combine like terms: -0.976281209 + 0.125 = -0.851281209 n = -0.851281209 Simplifying n = -0.851281209Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.101281209, -0.851281209}
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