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Simplifying 10n2 + -35 = 64n Reorder the terms: -35 + 10n2 = 64n Solving -35 + 10n2 = 64n Solving for variable 'n'. Reorder the terms: -35 + -64n + 10n2 = 64n + -64n Combine like terms: 64n + -64n = 0 -35 + -64n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.5 + -6.4n + n2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -6.4n + 3.5 + n2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -6.4n + n2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -6.4n + n2 = 0 + 3.5 -6.4n + n2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -6.4n + n2 = 3.5 The n term is -6.4n. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4n + 10.24 + n2 = 3.5 + 10.24 Reorder the terms: 10.24 + -6.4n + n2 = 3.5 + 10.24 Combine like terms: 3.5 + 10.24 = 13.74 10.24 + -6.4n + n2 = 13.74 Factor a perfect square on the left side: (n + -3.2)(n + -3.2) = 13.74 Calculate the square root of the right side: 3.706750599 Break this problem into two subproblems by setting (n + -3.2) equal to 3.706750599 and -3.706750599.Subproblem 1
n + -3.2 = 3.706750599 Simplifying n + -3.2 = 3.706750599 Reorder the terms: -3.2 + n = 3.706750599 Solving -3.2 + n = 3.706750599 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + n = 3.706750599 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + n = 3.706750599 + 3.2 n = 3.706750599 + 3.2 Combine like terms: 3.706750599 + 3.2 = 6.906750599 n = 6.906750599 Simplifying n = 6.906750599Subproblem 2
n + -3.2 = -3.706750599 Simplifying n + -3.2 = -3.706750599 Reorder the terms: -3.2 + n = -3.706750599 Solving -3.2 + n = -3.706750599 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + n = -3.706750599 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + n = -3.706750599 + 3.2 n = -3.706750599 + 3.2 Combine like terms: -3.706750599 + 3.2 = -0.506750599 n = -0.506750599 Simplifying n = -0.506750599Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.906750599, -0.506750599}
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