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Simplifying 3n(n + -5) = 50 Reorder the terms: 3n(-5 + n) = 50 (-5 * 3n + n * 3n) = 50 (-15n + 3n2) = 50 Solving -15n + 3n2 = 50 Solving for variable 'n'. Reorder the terms: -50 + -15n + 3n2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -15n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -5n + n2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -5n + 16.66666667 + n2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -5n + n2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -5n + n2 = 0 + 16.66666667 -5n + n2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -5n + n2 = 16.66666667 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 16.66666667 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 16.66666667 + 6.25 Combine like terms: 16.66666667 + 6.25 = 22.91666667 6.25 + -5n + n2 = 22.91666667 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 22.91666667 Calculate the square root of the right side: 4.787135539 Break this problem into two subproblems by setting (n + -2.5) equal to 4.787135539 and -4.787135539.Subproblem 1
n + -2.5 = 4.787135539 Simplifying n + -2.5 = 4.787135539 Reorder the terms: -2.5 + n = 4.787135539 Solving -2.5 + n = 4.787135539 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 4.787135539 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 4.787135539 + 2.5 n = 4.787135539 + 2.5 Combine like terms: 4.787135539 + 2.5 = 7.287135539 n = 7.287135539 Simplifying n = 7.287135539Subproblem 2
n + -2.5 = -4.787135539 Simplifying n + -2.5 = -4.787135539 Reorder the terms: -2.5 + n = -4.787135539 Solving -2.5 + n = -4.787135539 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -4.787135539 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -4.787135539 + 2.5 n = -4.787135539 + 2.5 Combine like terms: -4.787135539 + 2.5 = -2.287135539 n = -2.287135539 Simplifying n = -2.287135539Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.287135539, -2.287135539}
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