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Simplifying 5 = n2 + -1n Reorder the terms: 5 = -1n + n2 Solving 5 = -1n + n2 Solving for variable 'n'. Reorder the terms: 5 + n + -1n2 = -1n + n + n2 + -1n2 Combine like terms: -1n + n = 0 5 + n + -1n2 = 0 + n2 + -1n2 5 + n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 5 + n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -1n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -1n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n + n2 = 0 + 5 -1n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1n + n2 = 5 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 5 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1n + n2 = 5.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (n + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
n + 0.5 = 2.291287847 Simplifying n + 0.5 = 2.291287847 Reorder the terms: 0.5 + n = 2.291287847 Solving 0.5 + n = 2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 2.291287847 + -0.5 n = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 n = 1.791287847 Simplifying n = 1.791287847Subproblem 2
n + 0.5 = -2.291287847 Simplifying n + 0.5 = -2.291287847 Reorder the terms: 0.5 + n = -2.291287847 Solving 0.5 + n = -2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -2.291287847 + -0.5 n = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 n = -2.791287847 Simplifying n = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.791287847, -2.791287847}
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