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Simplifying -1n2 + -15n + 50 = 0 Reorder the terms: 50 + -15n + -1n2 = 0 Solving 50 + -15n + -1n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 15n + n2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 15n + 50 + n2 = 0 + 50 Reorder the terms: -50 + 50 + 15n + n2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 15n + n2 = 0 + 50 15n + n2 = 0 + 50 Combine like terms: 0 + 50 = 50 15n + n2 = 50 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 = 50 + 56.25 Reorder the terms: 56.25 + 15n + n2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + 15n + n2 = 106.25 Factor a perfect square on the left side: (n + 7.5)(n + 7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (n + 7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
n + 7.5 = 10.307764064 Simplifying n + 7.5 = 10.307764064 Reorder the terms: 7.5 + n = 10.307764064 Solving 7.5 + n = 10.307764064 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 = 10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + n = 10.307764064 + -7.5 n = 10.307764064 + -7.5 Combine like terms: 10.307764064 + -7.5 = 2.807764064 n = 2.807764064 Simplifying n = 2.807764064Subproblem 2
n + 7.5 = -10.307764064 Simplifying n + 7.5 = -10.307764064 Reorder the terms: 7.5 + n = -10.307764064 Solving 7.5 + n = -10.307764064 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 = -10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + n = -10.307764064 + -7.5 n = -10.307764064 + -7.5 Combine like terms: -10.307764064 + -7.5 = -17.807764064 n = -17.807764064 Simplifying n = -17.807764064Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.807764064, -17.807764064}
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