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Simplifying n(n + 7) = 94 Reorder the terms: n(7 + n) = 94 (7 * n + n * n) = 94 (7n + n2) = 94 Solving 7n + n2 = 94 Solving for variable 'n'. Reorder the terms: -94 + 7n + n2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 7n + 94 + n2 = 0 + 94 Reorder the terms: -94 + 94 + 7n + n2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 7n + n2 = 0 + 94 7n + n2 = 0 + 94 Combine like terms: 0 + 94 = 94 7n + n2 = 94 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 = 94 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 94 + 12.25 Combine like terms: 94 + 12.25 = 106.25 12.25 + 7n + n2 = 106.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (n + 3.5) equal to 10.307764064 and -10.307764064.Subproblem 1
n + 3.5 = 10.307764064 Simplifying n + 3.5 = 10.307764064 Reorder the terms: 3.5 + n = 10.307764064 Solving 3.5 + n = 10.307764064 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 = 10.307764064 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 10.307764064 + -3.5 n = 10.307764064 + -3.5 Combine like terms: 10.307764064 + -3.5 = 6.807764064 n = 6.807764064 Simplifying n = 6.807764064Subproblem 2
n + 3.5 = -10.307764064 Simplifying n + 3.5 = -10.307764064 Reorder the terms: 3.5 + n = -10.307764064 Solving 3.5 + n = -10.307764064 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 = -10.307764064 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -10.307764064 + -3.5 n = -10.307764064 + -3.5 Combine like terms: -10.307764064 + -3.5 = -13.807764064 n = -13.807764064 Simplifying n = -13.807764064Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.807764064, -13.807764064}
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