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Simplifying 0 = n2 + 16n + -63 Reorder the terms: 0 = -63 + 16n + n2 Solving 0 = -63 + 16n + n2 Solving for variable 'n'. Combine like terms: 0 + 63 = 63 63 + -16n + -1n2 = -63 + 16n + n2 + 63 + -16n + -1n2 Reorder the terms: 63 + -16n + -1n2 = -63 + 63 + 16n + -16n + n2 + -1n2 Combine like terms: -63 + 63 = 0 63 + -16n + -1n2 = 0 + 16n + -16n + n2 + -1n2 63 + -16n + -1n2 = 16n + -16n + n2 + -1n2 Combine like terms: 16n + -16n = 0 63 + -16n + -1n2 = 0 + n2 + -1n2 63 + -16n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 63 + -16n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 16n + n2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 16n + 63 + n2 = 0 + 63 Reorder the terms: -63 + 63 + 16n + n2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 16n + n2 = 0 + 63 16n + n2 = 0 + 63 Combine like terms: 0 + 63 = 63 16n + n2 = 63 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 = 63 + 64 Reorder the terms: 64 + 16n + n2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + 16n + n2 = 127 Factor a perfect square on the left side: (n + 8)(n + 8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (n + 8) equal to 11.26942767 and -11.26942767.Subproblem 1
n + 8 = 11.26942767 Simplifying n + 8 = 11.26942767 Reorder the terms: 8 + n = 11.26942767 Solving 8 + n = 11.26942767 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 = 11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + n = 11.26942767 + -8 n = 11.26942767 + -8 Combine like terms: 11.26942767 + -8 = 3.26942767 n = 3.26942767 Simplifying n = 3.26942767Subproblem 2
n + 8 = -11.26942767 Simplifying n + 8 = -11.26942767 Reorder the terms: 8 + n = -11.26942767 Solving 8 + n = -11.26942767 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 = -11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + n = -11.26942767 + -8 n = -11.26942767 + -8 Combine like terms: -11.26942767 + -8 = -19.26942767 n = -19.26942767 Simplifying n = -19.26942767Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.26942767, -19.26942767}
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