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Simplifying n2 + 7n = 240 Reorder the terms: 7n + n2 = 240 Solving 7n + n2 = 240 Solving for variable 'n'. Reorder the terms: -240 + 7n + n2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 7n + 240 + n2 = 0 + 240 Reorder the terms: -240 + 240 + 7n + n2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 7n + n2 = 0 + 240 7n + n2 = 0 + 240 Combine like terms: 0 + 240 = 240 7n + n2 = 240 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 240 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 240 + 12.25 Combine like terms: 240 + 12.25 = 252.25 12.25 + 7n + n2 = 252.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (n + 3.5) equal to 15.882380174 and -15.882380174.Subproblem 1
n + 3.5 = 15.882380174 Simplifying n + 3.5 = 15.882380174 Reorder the terms: 3.5 + n = 15.882380174 Solving 3.5 + n = 15.882380174 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 15.882380174 + -3.5 n = 15.882380174 + -3.5 Combine like terms: 15.882380174 + -3.5 = 12.382380174 n = 12.382380174 Simplifying n = 12.382380174Subproblem 2
n + 3.5 = -15.882380174 Simplifying n + 3.5 = -15.882380174 Reorder the terms: 3.5 + n = -15.882380174 Solving 3.5 + n = -15.882380174 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -15.882380174 + -3.5 n = -15.882380174 + -3.5 Combine like terms: -15.882380174 + -3.5 = -19.382380174 n = -19.382380174 Simplifying n = -19.382380174Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.382380174, -19.382380174}
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