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Simplifying n2 + -1n + -90 = 90 Reorder the terms: -90 + -1n + n2 = 90 Solving -90 + -1n + n2 = 90 Solving for variable 'n'. Reorder the terms: -90 + -90 + -1n + n2 = 90 + -90 Combine like terms: -90 + -90 = -180 -180 + -1n + n2 = 90 + -90 Combine like terms: 90 + -90 = 0 -180 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -1n + 180 + n2 = 0 + 180 Reorder the terms: -180 + 180 + -1n + n2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -1n + n2 = 0 + 180 -1n + n2 = 0 + 180 Combine like terms: 0 + 180 = 180 -1n + n2 = 180 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 = 180 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 180 + 0.25 Combine like terms: 180 + 0.25 = 180.25 0.25 + -1n + n2 = 180.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (n + -0.5) equal to 13.425721582 and -13.425721582.Subproblem 1
n + -0.5 = 13.425721582 Simplifying n + -0.5 = 13.425721582 Reorder the terms: -0.5 + n = 13.425721582 Solving -0.5 + n = 13.425721582 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 = 13.425721582 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 13.425721582 + 0.5 n = 13.425721582 + 0.5 Combine like terms: 13.425721582 + 0.5 = 13.925721582 n = 13.925721582 Simplifying n = 13.925721582Subproblem 2
n + -0.5 = -13.425721582 Simplifying n + -0.5 = -13.425721582 Reorder the terms: -0.5 + n = -13.425721582 Solving -0.5 + n = -13.425721582 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 = -13.425721582 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -13.425721582 + 0.5 n = -13.425721582 + 0.5 Combine like terms: -13.425721582 + 0.5 = -12.925721582 n = -12.925721582 Simplifying n = -12.925721582Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.925721582, -12.925721582}
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