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Simplifying 3n2 + -6n + -47 = -10 Reorder the terms: -47 + -6n + 3n2 = -10 Solving -47 + -6n + 3n2 = -10 Solving for variable 'n'. Reorder the terms: -47 + 10 + -6n + 3n2 = -10 + 10 Combine like terms: -47 + 10 = -37 -37 + -6n + 3n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -37 + -6n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12.33333333 + -2n + n2 = 0 Move the constant term to the right: Add '12.33333333' to each side of the equation. -12.33333333 + -2n + 12.33333333 + n2 = 0 + 12.33333333 Reorder the terms: -12.33333333 + 12.33333333 + -2n + n2 = 0 + 12.33333333 Combine like terms: -12.33333333 + 12.33333333 = 0.00000000 0.00000000 + -2n + n2 = 0 + 12.33333333 -2n + n2 = 0 + 12.33333333 Combine like terms: 0 + 12.33333333 = 12.33333333 -2n + n2 = 12.33333333 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 12.33333333 + 1 Reorder the terms: 1 + -2n + n2 = 12.33333333 + 1 Combine like terms: 12.33333333 + 1 = 13.33333333 1 + -2n + n2 = 13.33333333 Factor a perfect square on the left side: (n + -1)(n + -1) = 13.33333333 Calculate the square root of the right side: 3.651483716 Break this problem into two subproblems by setting (n + -1) equal to 3.651483716 and -3.651483716.Subproblem 1
n + -1 = 3.651483716 Simplifying n + -1 = 3.651483716 Reorder the terms: -1 + n = 3.651483716 Solving -1 + n = 3.651483716 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 3.651483716 + 1 Combine like terms: -1 + 1 = 0 0 + n = 3.651483716 + 1 n = 3.651483716 + 1 Combine like terms: 3.651483716 + 1 = 4.651483716 n = 4.651483716 Simplifying n = 4.651483716Subproblem 2
n + -1 = -3.651483716 Simplifying n + -1 = -3.651483716 Reorder the terms: -1 + n = -3.651483716 Solving -1 + n = -3.651483716 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -3.651483716 + 1 Combine like terms: -1 + 1 = 0 0 + n = -3.651483716 + 1 n = -3.651483716 + 1 Combine like terms: -3.651483716 + 1 = -2.651483716 n = -2.651483716 Simplifying n = -2.651483716Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.651483716, -2.651483716}
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