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Simplifying n2 + 72n + 36 = 0 Reorder the terms: 36 + 72n + n2 = 0 Solving 36 + 72n + 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 + 72n + -36 + n2 = 0 + -36 Reorder the terms: 36 + -36 + 72n + n2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 72n + n2 = 0 + -36 72n + n2 = 0 + -36 Combine like terms: 0 + -36 = -36 72n + n2 = -36 The n term is 72n. Take half its coefficient (36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. 72n + 1296 + n2 = -36 + 1296 Reorder the terms: 1296 + 72n + n2 = -36 + 1296 Combine like terms: -36 + 1296 = 1260 1296 + 72n + n2 = 1260 Factor a perfect square on the left side: (n + 36)(n + 36) = 1260 Calculate the square root of the right side: 35.496478699 Break this problem into two subproblems by setting (n + 36) equal to 35.496478699 and -35.496478699.Subproblem 1
n + 36 = 35.496478699 Simplifying n + 36 = 35.496478699 Reorder the terms: 36 + n = 35.496478699 Solving 36 + n = 35.496478699 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + n = 35.496478699 + -36 Combine like terms: 36 + -36 = 0 0 + n = 35.496478699 + -36 n = 35.496478699 + -36 Combine like terms: 35.496478699 + -36 = -0.503521301 n = -0.503521301 Simplifying n = -0.503521301Subproblem 2
n + 36 = -35.496478699 Simplifying n + 36 = -35.496478699 Reorder the terms: 36 + n = -35.496478699 Solving 36 + n = -35.496478699 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + n = -35.496478699 + -36 Combine like terms: 36 + -36 = 0 0 + n = -35.496478699 + -36 n = -35.496478699 + -36 Combine like terms: -35.496478699 + -36 = -71.496478699 n = -71.496478699 Simplifying n = -71.496478699Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.503521301, -71.496478699}
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