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Simplifying -72n2 + 127n + 72 = 0 Reorder the terms: 72 + 127n + -72n2 = 0 Solving 72 + 127n + -72n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -72 the coefficient of the squared term: Divide each side by '-72'. -1 + -1.763888889n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.763888889n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -1.763888889n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.763888889n + n2 = 0 + 1 -1.763888889n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.763888889n + n2 = 1 The n term is -1.763888889n. Take half its coefficient (-0.8819444445). Square it (0.7778260032) and add it to both sides. Add '0.7778260032' to each side of the equation. -1.763888889n + 0.7778260032 + n2 = 1 + 0.7778260032 Reorder the terms: 0.7778260032 + -1.763888889n + n2 = 1 + 0.7778260032 Combine like terms: 1 + 0.7778260032 = 1.7778260032 0.7778260032 + -1.763888889n + n2 = 1.7778260032 Factor a perfect square on the left side: (n + -0.8819444445)(n + -0.8819444445) = 1.7778260032 Calculate the square root of the right side: 1.333351418 Break this problem into two subproblems by setting (n + -0.8819444445) equal to 1.333351418 and -1.333351418.Subproblem 1
n + -0.8819444445 = 1.333351418 Simplifying n + -0.8819444445 = 1.333351418 Reorder the terms: -0.8819444445 + n = 1.333351418 Solving -0.8819444445 + n = 1.333351418 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8819444445' to each side of the equation. -0.8819444445 + 0.8819444445 + n = 1.333351418 + 0.8819444445 Combine like terms: -0.8819444445 + 0.8819444445 = 0.0000000000 0.0000000000 + n = 1.333351418 + 0.8819444445 n = 1.333351418 + 0.8819444445 Combine like terms: 1.333351418 + 0.8819444445 = 2.2152958625 n = 2.2152958625 Simplifying n = 2.2152958625Subproblem 2
n + -0.8819444445 = -1.333351418 Simplifying n + -0.8819444445 = -1.333351418 Reorder the terms: -0.8819444445 + n = -1.333351418 Solving -0.8819444445 + n = -1.333351418 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8819444445' to each side of the equation. -0.8819444445 + 0.8819444445 + n = -1.333351418 + 0.8819444445 Combine like terms: -0.8819444445 + 0.8819444445 = 0.0000000000 0.0000000000 + n = -1.333351418 + 0.8819444445 n = -1.333351418 + 0.8819444445 Combine like terms: -1.333351418 + 0.8819444445 = -0.4514069735 n = -0.4514069735 Simplifying n = -0.4514069735Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.2152958625, -0.4514069735}
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