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Simplifying n2 + -135n + 720 = 0 Reorder the terms: 720 + -135n + n2 = 0 Solving 720 + -135n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + -135n + -720 + n2 = 0 + -720 Reorder the terms: 720 + -720 + -135n + n2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -135n + n2 = 0 + -720 -135n + n2 = 0 + -720 Combine like terms: 0 + -720 = -720 -135n + n2 = -720 The n term is -135n. Take half its coefficient (-67.5). Square it (4556.25) and add it to both sides. Add '4556.25' to each side of the equation. -135n + 4556.25 + n2 = -720 + 4556.25 Reorder the terms: 4556.25 + -135n + n2 = -720 + 4556.25 Combine like terms: -720 + 4556.25 = 3836.25 4556.25 + -135n + n2 = 3836.25 Factor a perfect square on the left side: (n + -67.5)(n + -67.5) = 3836.25 Calculate the square root of the right side: 61.937468466 Break this problem into two subproblems by setting (n + -67.5) equal to 61.937468466 and -61.937468466.Subproblem 1
n + -67.5 = 61.937468466 Simplifying n + -67.5 = 61.937468466 Reorder the terms: -67.5 + n = 61.937468466 Solving -67.5 + n = 61.937468466 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '67.5' to each side of the equation. -67.5 + 67.5 + n = 61.937468466 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + n = 61.937468466 + 67.5 n = 61.937468466 + 67.5 Combine like terms: 61.937468466 + 67.5 = 129.437468466 n = 129.437468466 Simplifying n = 129.437468466Subproblem 2
n + -67.5 = -61.937468466 Simplifying n + -67.5 = -61.937468466 Reorder the terms: -67.5 + n = -61.937468466 Solving -67.5 + n = -61.937468466 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '67.5' to each side of the equation. -67.5 + 67.5 + n = -61.937468466 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + n = -61.937468466 + 67.5 n = -61.937468466 + 67.5 Combine like terms: -61.937468466 + 67.5 = 5.562531534 n = 5.562531534 Simplifying n = 5.562531534Solution
The solution to the problem is based on the solutions from the subproblems. n = {129.437468466, 5.562531534}
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