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Simplifying n2 + -19n + 72 = 0 Reorder the terms: 72 + -19n + n2 = 0 Solving 72 + -19n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -19n + -72 + n2 = 0 + -72 Reorder the terms: 72 + -72 + -19n + n2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -19n + n2 = 0 + -72 -19n + n2 = 0 + -72 Combine like terms: 0 + -72 = -72 -19n + n2 = -72 The n term is -19n. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19n + 90.25 + n2 = -72 + 90.25 Reorder the terms: 90.25 + -19n + n2 = -72 + 90.25 Combine like terms: -72 + 90.25 = 18.25 90.25 + -19n + n2 = 18.25 Factor a perfect square on the left side: (n + -9.5)(n + -9.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (n + -9.5) equal to 4.272001873 and -4.272001873.Subproblem 1
n + -9.5 = 4.272001873 Simplifying n + -9.5 = 4.272001873 Reorder the terms: -9.5 + n = 4.272001873 Solving -9.5 + n = 4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + n = 4.272001873 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + n = 4.272001873 + 9.5 n = 4.272001873 + 9.5 Combine like terms: 4.272001873 + 9.5 = 13.772001873 n = 13.772001873 Simplifying n = 13.772001873Subproblem 2
n + -9.5 = -4.272001873 Simplifying n + -9.5 = -4.272001873 Reorder the terms: -9.5 + n = -4.272001873 Solving -9.5 + n = -4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + n = -4.272001873 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + n = -4.272001873 + 9.5 n = -4.272001873 + 9.5 Combine like terms: -4.272001873 + 9.5 = 5.227998127 n = 5.227998127 Simplifying n = 5.227998127Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.772001873, 5.227998127}
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