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Simplifying n2 + -15n + -24 = 0 Reorder the terms: -24 + -15n + n2 = 0 Solving -24 + -15n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -15n + 24 + n2 = 0 + 24 Reorder the terms: -24 + 24 + -15n + n2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -15n + n2 = 0 + 24 -15n + n2 = 0 + 24 Combine like terms: 0 + 24 = 24 -15n + n2 = 24 The n term is -15n. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15n + 56.25 + n2 = 24 + 56.25 Reorder the terms: 56.25 + -15n + n2 = 24 + 56.25 Combine like terms: 24 + 56.25 = 80.25 56.25 + -15n + n2 = 80.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (n + -7.5) equal to 8.958236434 and -8.958236434.Subproblem 1
n + -7.5 = 8.958236434 Simplifying n + -7.5 = 8.958236434 Reorder the terms: -7.5 + n = 8.958236434 Solving -7.5 + n = 8.958236434 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 8.958236434 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 8.958236434 + 7.5 n = 8.958236434 + 7.5 Combine like terms: 8.958236434 + 7.5 = 16.458236434 n = 16.458236434 Simplifying n = 16.458236434Subproblem 2
n + -7.5 = -8.958236434 Simplifying n + -7.5 = -8.958236434 Reorder the terms: -7.5 + n = -8.958236434 Solving -7.5 + n = -8.958236434 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -8.958236434 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -8.958236434 + 7.5 n = -8.958236434 + 7.5 Combine like terms: -8.958236434 + 7.5 = -1.458236434 n = -1.458236434 Simplifying n = -1.458236434Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.458236434, -1.458236434}
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