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Simplifying n2 + 10n + -37 = 0 Reorder the terms: -37 + 10n + n2 = 0 Solving -37 + 10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 10n + 37 + n2 = 0 + 37 Reorder the terms: -37 + 37 + 10n + n2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 10n + n2 = 0 + 37 10n + n2 = 0 + 37 Combine like terms: 0 + 37 = 37 10n + n2 = 37 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = 37 + 25 Reorder the terms: 25 + 10n + n2 = 37 + 25 Combine like terms: 37 + 25 = 62 25 + 10n + n2 = 62 Factor a perfect square on the left side: (n + 5)(n + 5) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (n + 5) equal to 7.874007874 and -7.874007874.Subproblem 1
n + 5 = 7.874007874 Simplifying n + 5 = 7.874007874 Reorder the terms: 5 + n = 7.874007874 Solving 5 + n = 7.874007874 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 7.874007874 + -5 Combine like terms: 5 + -5 = 0 0 + n = 7.874007874 + -5 n = 7.874007874 + -5 Combine like terms: 7.874007874 + -5 = 2.874007874 n = 2.874007874 Simplifying n = 2.874007874Subproblem 2
n + 5 = -7.874007874 Simplifying n + 5 = -7.874007874 Reorder the terms: 5 + n = -7.874007874 Solving 5 + n = -7.874007874 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -7.874007874 + -5 Combine like terms: 5 + -5 = 0 0 + n = -7.874007874 + -5 n = -7.874007874 + -5 Combine like terms: -7.874007874 + -5 = -12.874007874 n = -12.874007874 Simplifying n = -12.874007874Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.874007874, -12.874007874}
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