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Simplifying n2 + -1n + -160 = 0 Reorder the terms: -160 + -1n + n2 = 0 Solving -160 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -1n + 160 + n2 = 0 + 160 Reorder the terms: -160 + 160 + -1n + n2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -1n + n2 = 0 + 160 -1n + n2 = 0 + 160 Combine like terms: 0 + 160 = 160 -1n + n2 = 160 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 = 160 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 160 + 0.25 Combine like terms: 160 + 0.25 = 160.25 0.25 + -1n + n2 = 160.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (n + -0.5) equal to 12.658988901 and -12.658988901.Subproblem 1
n + -0.5 = 12.658988901 Simplifying n + -0.5 = 12.658988901 Reorder the terms: -0.5 + n = 12.658988901 Solving -0.5 + n = 12.658988901 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 = 12.658988901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 12.658988901 + 0.5 n = 12.658988901 + 0.5 Combine like terms: 12.658988901 + 0.5 = 13.158988901 n = 13.158988901 Simplifying n = 13.158988901Subproblem 2
n + -0.5 = -12.658988901 Simplifying n + -0.5 = -12.658988901 Reorder the terms: -0.5 + n = -12.658988901 Solving -0.5 + n = -12.658988901 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 = -12.658988901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -12.658988901 + 0.5 n = -12.658988901 + 0.5 Combine like terms: -12.658988901 + 0.5 = -12.158988901 n = -12.158988901 Simplifying n = -12.158988901Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.158988901, -12.158988901}
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