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Simplifying n2 + -1n + -96 = 0 Reorder the terms: -96 + -1n + n2 = 0 Solving -96 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -1n + 96 + n2 = 0 + 96 Reorder the terms: -96 + 96 + -1n + n2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -1n + n2 = 0 + 96 -1n + n2 = 0 + 96 Combine like terms: 0 + 96 = 96 -1n + n2 = 96 The n term is -1n. 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 = 96 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 96 + 0.25 Combine like terms: 96 + 0.25 = 96.25 0.25 + -1n + n2 = 96.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (n + -0.5) equal to 9.810708435 and -9.810708435.Subproblem 1
n + -0.5 = 9.810708435 Simplifying n + -0.5 = 9.810708435 Reorder the terms: -0.5 + n = 9.810708435 Solving -0.5 + n = 9.810708435 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 = 9.810708435 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 9.810708435 + 0.5 n = 9.810708435 + 0.5 Combine like terms: 9.810708435 + 0.5 = 10.310708435 n = 10.310708435 Simplifying n = 10.310708435Subproblem 2
n + -0.5 = -9.810708435 Simplifying n + -0.5 = -9.810708435 Reorder the terms: -0.5 + n = -9.810708435 Solving -0.5 + n = -9.810708435 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 = -9.810708435 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -9.810708435 + 0.5 n = -9.810708435 + 0.5 Combine like terms: -9.810708435 + 0.5 = -9.310708435 n = -9.310708435 Simplifying n = -9.310708435Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.310708435, -9.310708435}
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