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Simplifying n2 + -16n + 36 = 0 Reorder the terms: 36 + -16n + n2 = 0 Solving 36 + -16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16n + -36 + n2 = 0 + -36 Reorder the terms: 36 + -36 + -16n + n2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16n + n2 = 0 + -36 -16n + n2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16n + n2 = -36 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 = -36 + 64 Reorder the terms: 64 + -16n + n2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + -16n + n2 = 28 Factor a perfect square on the left side: (n + -8)(n + -8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (n + -8) equal to 5.291502622 and -5.291502622.Subproblem 1
n + -8 = 5.291502622 Simplifying n + -8 = 5.291502622 Reorder the terms: -8 + n = 5.291502622 Solving -8 + n = 5.291502622 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 = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + n = 5.291502622 + 8 n = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 n = 13.291502622 Simplifying n = 13.291502622Subproblem 2
n + -8 = -5.291502622 Simplifying n + -8 = -5.291502622 Reorder the terms: -8 + n = -5.291502622 Solving -8 + n = -5.291502622 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 = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + n = -5.291502622 + 8 n = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 n = 2.708497378 Simplifying n = 2.708497378Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.291502622, 2.708497378}
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