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Simplifying -1n2 + 16n = -1100 Reorder the terms: 16n + -1n2 = -1100 Solving 16n + -1n2 = -1100 Solving for variable 'n'. Reorder the terms: 1100 + 16n + -1n2 = -1100 + 1100 Combine like terms: -1100 + 1100 = 0 1100 + 16n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1100 + -16n + n2 = 0 Move the constant term to the right: Add '1100' to each side of the equation. -1100 + -16n + 1100 + n2 = 0 + 1100 Reorder the terms: -1100 + 1100 + -16n + n2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + -16n + n2 = 0 + 1100 -16n + n2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 -16n + n2 = 1100 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 = 1100 + 64 Reorder the terms: 64 + -16n + n2 = 1100 + 64 Combine like terms: 1100 + 64 = 1164 64 + -16n + n2 = 1164 Factor a perfect square on the left side: (n + -8)(n + -8) = 1164 Calculate the square root of the right side: 34.117444218 Break this problem into two subproblems by setting (n + -8) equal to 34.117444218 and -34.117444218.Subproblem 1
n + -8 = 34.117444218 Simplifying n + -8 = 34.117444218 Reorder the terms: -8 + n = 34.117444218 Solving -8 + n = 34.117444218 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 = 34.117444218 + 8 Combine like terms: -8 + 8 = 0 0 + n = 34.117444218 + 8 n = 34.117444218 + 8 Combine like terms: 34.117444218 + 8 = 42.117444218 n = 42.117444218 Simplifying n = 42.117444218Subproblem 2
n + -8 = -34.117444218 Simplifying n + -8 = -34.117444218 Reorder the terms: -8 + n = -34.117444218 Solving -8 + n = -34.117444218 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 = -34.117444218 + 8 Combine like terms: -8 + 8 = 0 0 + n = -34.117444218 + 8 n = -34.117444218 + 8 Combine like terms: -34.117444218 + 8 = -26.117444218 n = -26.117444218 Simplifying n = -26.117444218Solution
The solution to the problem is based on the solutions from the subproblems. n = {42.117444218, -26.117444218}
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