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Simplifying n(n + -10) = 69.5 Reorder the terms: n(-10 + n) = 69.5 (-10 * n + n * n) = 69.5 (-10n + n2) = 69.5 Solving -10n + n2 = 69.5 Solving for variable 'n'. Reorder the terms: -69.5 + -10n + n2 = 69.5 + -69.5 Combine like terms: 69.5 + -69.5 = 0.0 -69.5 + -10n + n2 = 0.0 Begin completing the square. Move the constant term to the right: Add '69.5' to each side of the equation. -69.5 + -10n + 69.5 + n2 = 0.0 + 69.5 Reorder the terms: -69.5 + 69.5 + -10n + n2 = 0.0 + 69.5 Combine like terms: -69.5 + 69.5 = 0.0 0.0 + -10n + n2 = 0.0 + 69.5 -10n + n2 = 0.0 + 69.5 Combine like terms: 0.0 + 69.5 = 69.5 -10n + n2 = 69.5 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 = 69.5 + 25 Reorder the terms: 25 + -10n + n2 = 69.5 + 25 Combine like terms: 69.5 + 25 = 94.5 25 + -10n + n2 = 94.5 Factor a perfect square on the left side: (n + -5)(n + -5) = 94.5 Calculate the square root of the right side: 9.721111048 Break this problem into two subproblems by setting (n + -5) equal to 9.721111048 and -9.721111048.Subproblem 1
n + -5 = 9.721111048 Simplifying n + -5 = 9.721111048 Reorder the terms: -5 + n = 9.721111048 Solving -5 + n = 9.721111048 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 = 9.721111048 + 5 Combine like terms: -5 + 5 = 0 0 + n = 9.721111048 + 5 n = 9.721111048 + 5 Combine like terms: 9.721111048 + 5 = 14.721111048 n = 14.721111048 Simplifying n = 14.721111048Subproblem 2
n + -5 = -9.721111048 Simplifying n + -5 = -9.721111048 Reorder the terms: -5 + n = -9.721111048 Solving -5 + n = -9.721111048 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 = -9.721111048 + 5 Combine like terms: -5 + 5 = 0 0 + n = -9.721111048 + 5 n = -9.721111048 + 5 Combine like terms: -9.721111048 + 5 = -4.721111048 n = -4.721111048 Simplifying n = -4.721111048Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.721111048, -4.721111048}
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