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Simplifying n2 + 13n = 240 Reorder the terms: 13n + n2 = 240 Solving 13n + n2 = 240 Solving for variable 'n'. Reorder the terms: -240 + 13n + n2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 13n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 13n + 240 + n2 = 0 + 240 Reorder the terms: -240 + 240 + 13n + n2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 13n + n2 = 0 + 240 13n + n2 = 0 + 240 Combine like terms: 0 + 240 = 240 13n + n2 = 240 The n term is 13n. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13n + 42.25 + n2 = 240 + 42.25 Reorder the terms: 42.25 + 13n + n2 = 240 + 42.25 Combine like terms: 240 + 42.25 = 282.25 42.25 + 13n + n2 = 282.25 Factor a perfect square on the left side: (n + 6.5)(n + 6.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (n + 6.5) equal to 16.800297616 and -16.800297616.Subproblem 1
n + 6.5 = 16.800297616 Simplifying n + 6.5 = 16.800297616 Reorder the terms: 6.5 + n = 16.800297616 Solving 6.5 + n = 16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = 16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = 16.800297616 + -6.5 n = 16.800297616 + -6.5 Combine like terms: 16.800297616 + -6.5 = 10.300297616 n = 10.300297616 Simplifying n = 10.300297616Subproblem 2
n + 6.5 = -16.800297616 Simplifying n + 6.5 = -16.800297616 Reorder the terms: 6.5 + n = -16.800297616 Solving 6.5 + n = -16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = -16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = -16.800297616 + -6.5 n = -16.800297616 + -6.5 Combine like terms: -16.800297616 + -6.5 = -23.300297616 n = -23.300297616 Simplifying n = -23.300297616Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.300297616, -23.300297616}
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