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Simplifying n2 + -16n = 60 Reorder the terms: -16n + n2 = 60 Solving -16n + n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + -16n + n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -16n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + -16n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -16n + n2 = 0 + 60 -16n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 -16n + n2 = 60 The n term is -16n. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16n + 64 + n2 = 60 + 64 Reorder the terms: 64 + -16n + n2 = 60 + 64 Combine like terms: 60 + 64 = 124 64 + -16n + n2 = 124 Factor a perfect square on the left side: (n + -8)(n + -8) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (n + -8) equal to 11.135528726 and -11.135528726.Subproblem 1
n + -8 = 11.135528726 Simplifying n + -8 = 11.135528726 Reorder the terms: -8 + n = 11.135528726 Solving -8 + n = 11.135528726 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = 11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + n = 11.135528726 + 8 n = 11.135528726 + 8 Combine like terms: 11.135528726 + 8 = 19.135528726 n = 19.135528726 Simplifying n = 19.135528726Subproblem 2
n + -8 = -11.135528726 Simplifying n + -8 = -11.135528726 Reorder the terms: -8 + n = -11.135528726 Solving -8 + n = -11.135528726 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = -11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + n = -11.135528726 + 8 n = -11.135528726 + 8 Combine like terms: -11.135528726 + 8 = -3.135528726 n = -3.135528726 Simplifying n = -3.135528726Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.135528726, -3.135528726}
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