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Simplifying 10n2 = 3n + 16 Reorder the terms: 10n2 = 16 + 3n Solving 10n2 = 16 + 3n Solving for variable 'n'. Reorder the terms: -16 + -3n + 10n2 = 16 + 3n + -16 + -3n Reorder the terms: -16 + -3n + 10n2 = 16 + -16 + 3n + -3n Combine like terms: 16 + -16 = 0 -16 + -3n + 10n2 = 0 + 3n + -3n -16 + -3n + 10n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -16 + -3n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.6 + -0.3n + n2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.3n + 1.6 + n2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.3n + n2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.3n + n2 = 0 + 1.6 -0.3n + n2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.3n + n2 = 1.6 The n term is -0.3n. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3n + 0.0225 + n2 = 1.6 + 0.0225 Reorder the terms: 0.0225 + -0.3n + n2 = 1.6 + 0.0225 Combine like terms: 1.6 + 0.0225 = 1.6225 0.0225 + -0.3n + n2 = 1.6225 Factor a perfect square on the left side: (n + -0.15)(n + -0.15) = 1.6225 Calculate the square root of the right side: 1.27377392 Break this problem into two subproblems by setting (n + -0.15) equal to 1.27377392 and -1.27377392.Subproblem 1
n + -0.15 = 1.27377392 Simplifying n + -0.15 = 1.27377392 Reorder the terms: -0.15 + n = 1.27377392 Solving -0.15 + n = 1.27377392 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + n = 1.27377392 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + n = 1.27377392 + 0.15 n = 1.27377392 + 0.15 Combine like terms: 1.27377392 + 0.15 = 1.42377392 n = 1.42377392 Simplifying n = 1.42377392Subproblem 2
n + -0.15 = -1.27377392 Simplifying n + -0.15 = -1.27377392 Reorder the terms: -0.15 + n = -1.27377392 Solving -0.15 + n = -1.27377392 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + n = -1.27377392 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + n = -1.27377392 + 0.15 n = -1.27377392 + 0.15 Combine like terms: -1.27377392 + 0.15 = -1.12377392 n = -1.12377392 Simplifying n = -1.12377392Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.42377392, -1.12377392}
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