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Simplifying n2 + 2n + -3 = 48 Reorder the terms: -3 + 2n + n2 = 48 Solving -3 + 2n + n2 = 48 Solving for variable 'n'. Reorder the terms: -3 + -48 + 2n + n2 = 48 + -48 Combine like terms: -3 + -48 = -51 -51 + 2n + n2 = 48 + -48 Combine like terms: 48 + -48 = 0 -51 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + 2n + 51 + n2 = 0 + 51 Reorder the terms: -51 + 51 + 2n + n2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 2n + n2 = 0 + 51 2n + n2 = 0 + 51 Combine like terms: 0 + 51 = 51 2n + n2 = 51 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 = 51 + 1 Reorder the terms: 1 + 2n + n2 = 51 + 1 Combine like terms: 51 + 1 = 52 1 + 2n + n2 = 52 Factor a perfect square on the left side: (n + 1)(n + 1) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (n + 1) equal to 7.211102551 and -7.211102551.Subproblem 1
n + 1 = 7.211102551 Simplifying n + 1 = 7.211102551 Reorder the terms: 1 + n = 7.211102551 Solving 1 + n = 7.211102551 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 = 7.211102551 + -1 Combine like terms: 1 + -1 = 0 0 + n = 7.211102551 + -1 n = 7.211102551 + -1 Combine like terms: 7.211102551 + -1 = 6.211102551 n = 6.211102551 Simplifying n = 6.211102551Subproblem 2
n + 1 = -7.211102551 Simplifying n + 1 = -7.211102551 Reorder the terms: 1 + n = -7.211102551 Solving 1 + n = -7.211102551 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 = -7.211102551 + -1 Combine like terms: 1 + -1 = 0 0 + n = -7.211102551 + -1 n = -7.211102551 + -1 Combine like terms: -7.211102551 + -1 = -8.211102551 n = -8.211102551 Simplifying n = -8.211102551Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.211102551, -8.211102551}
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