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Simplifying n2 = -36n + 15 Reorder the terms: n2 = 15 + -36n Solving n2 = 15 + -36n Solving for variable 'n'. Reorder the terms: -15 + 36n + n2 = 15 + -36n + -15 + 36n Reorder the terms: -15 + 36n + n2 = 15 + -15 + -36n + 36n Combine like terms: 15 + -15 = 0 -15 + 36n + n2 = 0 + -36n + 36n -15 + 36n + n2 = -36n + 36n Combine like terms: -36n + 36n = 0 -15 + 36n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 36n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + 36n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 36n + n2 = 0 + 15 36n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 36n + n2 = 15 The n term is 36n. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36n + 324 + n2 = 15 + 324 Reorder the terms: 324 + 36n + n2 = 15 + 324 Combine like terms: 15 + 324 = 339 324 + 36n + n2 = 339 Factor a perfect square on the left side: (n + 18)(n + 18) = 339 Calculate the square root of the right side: 18.41195264 Break this problem into two subproblems by setting (n + 18) equal to 18.41195264 and -18.41195264.Subproblem 1
n + 18 = 18.41195264 Simplifying n + 18 = 18.41195264 Reorder the terms: 18 + n = 18.41195264 Solving 18 + n = 18.41195264 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + n = 18.41195264 + -18 Combine like terms: 18 + -18 = 0 0 + n = 18.41195264 + -18 n = 18.41195264 + -18 Combine like terms: 18.41195264 + -18 = 0.41195264 n = 0.41195264 Simplifying n = 0.41195264Subproblem 2
n + 18 = -18.41195264 Simplifying n + 18 = -18.41195264 Reorder the terms: 18 + n = -18.41195264 Solving 18 + n = -18.41195264 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + n = -18.41195264 + -18 Combine like terms: 18 + -18 = 0 0 + n = -18.41195264 + -18 n = -18.41195264 + -18 Combine like terms: -18.41195264 + -18 = -36.41195264 n = -36.41195264 Simplifying n = -36.41195264Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.41195264, -36.41195264}
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