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Simplifying n2 + 8 + -15n = 0 Reorder the terms: 8 + -15n + n2 = 0 Solving 8 + -15n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -15n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + -15n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -15n + n2 = 0 + -8 -15n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 -15n + n2 = -8 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 = -8 + 56.25 Reorder the terms: 56.25 + -15n + n2 = -8 + 56.25 Combine like terms: -8 + 56.25 = 48.25 56.25 + -15n + n2 = 48.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (n + -7.5) equal to 6.946221995 and -6.946221995.Subproblem 1
n + -7.5 = 6.946221995 Simplifying n + -7.5 = 6.946221995 Reorder the terms: -7.5 + n = 6.946221995 Solving -7.5 + n = 6.946221995 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 = 6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 6.946221995 + 7.5 n = 6.946221995 + 7.5 Combine like terms: 6.946221995 + 7.5 = 14.446221995 n = 14.446221995 Simplifying n = 14.446221995Subproblem 2
n + -7.5 = -6.946221995 Simplifying n + -7.5 = -6.946221995 Reorder the terms: -7.5 + n = -6.946221995 Solving -7.5 + n = -6.946221995 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 = -6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -6.946221995 + 7.5 n = -6.946221995 + 7.5 Combine like terms: -6.946221995 + 7.5 = 0.553778005 n = 0.553778005 Simplifying n = 0.553778005Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.446221995, 0.553778005}
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