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Simplifying n2 + -134n + 132 = 0 Reorder the terms: 132 + -134n + n2 = 0 Solving 132 + -134n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-132' to each side of the equation. 132 + -134n + -132 + n2 = 0 + -132 Reorder the terms: 132 + -132 + -134n + n2 = 0 + -132 Combine like terms: 132 + -132 = 0 0 + -134n + n2 = 0 + -132 -134n + n2 = 0 + -132 Combine like terms: 0 + -132 = -132 -134n + n2 = -132 The n term is -134n. Take half its coefficient (-67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. -134n + 4489 + n2 = -132 + 4489 Reorder the terms: 4489 + -134n + n2 = -132 + 4489 Combine like terms: -132 + 4489 = 4357 4489 + -134n + n2 = 4357 Factor a perfect square on the left side: (n + -67)(n + -67) = 4357 Calculate the square root of the right side: 66.007575323 Break this problem into two subproblems by setting (n + -67) equal to 66.007575323 and -66.007575323.Subproblem 1
n + -67 = 66.007575323 Simplifying n + -67 = 66.007575323 Reorder the terms: -67 + n = 66.007575323 Solving -67 + n = 66.007575323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + n = 66.007575323 + 67 Combine like terms: -67 + 67 = 0 0 + n = 66.007575323 + 67 n = 66.007575323 + 67 Combine like terms: 66.007575323 + 67 = 133.007575323 n = 133.007575323 Simplifying n = 133.007575323Subproblem 2
n + -67 = -66.007575323 Simplifying n + -67 = -66.007575323 Reorder the terms: -67 + n = -66.007575323 Solving -67 + n = -66.007575323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '67' to each side of the equation. -67 + 67 + n = -66.007575323 + 67 Combine like terms: -67 + 67 = 0 0 + n = -66.007575323 + 67 n = -66.007575323 + 67 Combine like terms: -66.007575323 + 67 = 0.992424677 n = 0.992424677 Simplifying n = 0.992424677Solution
The solution to the problem is based on the solutions from the subproblems. n = {133.007575323, 0.992424677}
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