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Simplifying 16n2 + -18n + -15 = 0 Reorder the terms: -15 + -18n + 16n2 = 0 Solving -15 + -18n + 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 + -1.125n + n2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -1.125n + 0.9375 + n2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -1.125n + n2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -1.125n + n2 = 0 + 0.9375 -1.125n + n2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -1.125n + n2 = 0.9375 The n term is -1.125n. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125n + 0.31640625 + n2 = 0.9375 + 0.31640625 Reorder the terms: 0.31640625 + -1.125n + n2 = 0.9375 + 0.31640625 Combine like terms: 0.9375 + 0.31640625 = 1.25390625 0.31640625 + -1.125n + n2 = 1.25390625 Factor a perfect square on the left side: (n + -0.5625)(n + -0.5625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (n + -0.5625) equal to 1.119779554 and -1.119779554.Subproblem 1
n + -0.5625 = 1.119779554 Simplifying n + -0.5625 = 1.119779554 Reorder the terms: -0.5625 + n = 1.119779554 Solving -0.5625 + n = 1.119779554 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = 1.119779554 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = 1.119779554 + 0.5625 n = 1.119779554 + 0.5625 Combine like terms: 1.119779554 + 0.5625 = 1.682279554 n = 1.682279554 Simplifying n = 1.682279554Subproblem 2
n + -0.5625 = -1.119779554 Simplifying n + -0.5625 = -1.119779554 Reorder the terms: -0.5625 + n = -1.119779554 Solving -0.5625 + n = -1.119779554 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + n = -1.119779554 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + n = -1.119779554 + 0.5625 n = -1.119779554 + 0.5625 Combine like terms: -1.119779554 + 0.5625 = -0.557279554 n = -0.557279554 Simplifying n = -0.557279554Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.682279554, -0.557279554}
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