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Simplifying 3n2 + -51n + -8 = 0 Reorder the terms: -8 + -51n + 3n2 = 0 Solving -8 + -51n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -17n + n2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -17n + 2.666666667 + n2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -17n + n2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -17n + n2 = 0 + 2.666666667 -17n + n2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -17n + n2 = 2.666666667 The n term is -17n. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17n + 72.25 + n2 = 2.666666667 + 72.25 Reorder the terms: 72.25 + -17n + n2 = 2.666666667 + 72.25 Combine like terms: 2.666666667 + 72.25 = 74.916666667 72.25 + -17n + n2 = 74.916666667 Factor a perfect square on the left side: (n + -8.5)(n + -8.5) = 74.916666667 Calculate the square root of the right side: 8.655441448 Break this problem into two subproblems by setting (n + -8.5) equal to 8.655441448 and -8.655441448.Subproblem 1
n + -8.5 = 8.655441448 Simplifying n + -8.5 = 8.655441448 Reorder the terms: -8.5 + n = 8.655441448 Solving -8.5 + n = 8.655441448 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + n = 8.655441448 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + n = 8.655441448 + 8.5 n = 8.655441448 + 8.5 Combine like terms: 8.655441448 + 8.5 = 17.155441448 n = 17.155441448 Simplifying n = 17.155441448Subproblem 2
n + -8.5 = -8.655441448 Simplifying n + -8.5 = -8.655441448 Reorder the terms: -8.5 + n = -8.655441448 Solving -8.5 + n = -8.655441448 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + n = -8.655441448 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + n = -8.655441448 + 8.5 n = -8.655441448 + 8.5 Combine like terms: -8.655441448 + 8.5 = -0.155441448 n = -0.155441448 Simplifying n = -0.155441448Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.155441448, -0.155441448}
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