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Simplifying 5n + 15 = n2 + 2 Reorder the terms: 15 + 5n = n2 + 2 Reorder the terms: 15 + 5n = 2 + n2 Solving 15 + 5n = 2 + n2 Solving for variable 'n'. Reorder the terms: 15 + -2 + 5n + -1n2 = 2 + n2 + -2 + -1n2 Combine like terms: 15 + -2 = 13 13 + 5n + -1n2 = 2 + n2 + -2 + -1n2 Reorder the terms: 13 + 5n + -1n2 = 2 + -2 + n2 + -1n2 Combine like terms: 2 + -2 = 0 13 + 5n + -1n2 = 0 + n2 + -1n2 13 + 5n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 13 + 5n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -5n + n2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -5n + 13 + n2 = 0 + 13 Reorder the terms: -13 + 13 + -5n + n2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -5n + n2 = 0 + 13 -5n + n2 = 0 + 13 Combine like terms: 0 + 13 = 13 -5n + n2 = 13 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 13 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 13 + 6.25 Combine like terms: 13 + 6.25 = 19.25 6.25 + -5n + n2 = 19.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (n + -2.5) equal to 4.387482194 and -4.387482194.Subproblem 1
n + -2.5 = 4.387482194 Simplifying n + -2.5 = 4.387482194 Reorder the terms: -2.5 + n = 4.387482194 Solving -2.5 + n = 4.387482194 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 4.387482194 + 2.5 n = 4.387482194 + 2.5 Combine like terms: 4.387482194 + 2.5 = 6.887482194 n = 6.887482194 Simplifying n = 6.887482194Subproblem 2
n + -2.5 = -4.387482194 Simplifying n + -2.5 = -4.387482194 Reorder the terms: -2.5 + n = -4.387482194 Solving -2.5 + n = -4.387482194 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -4.387482194 + 2.5 n = -4.387482194 + 2.5 Combine like terms: -4.387482194 + 2.5 = -1.887482194 n = -1.887482194 Simplifying n = -1.887482194Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.887482194, -1.887482194}
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