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Simplifying n2 + -2n + -35 = 7 Reorder the terms: -35 + -2n + n2 = 7 Solving -35 + -2n + n2 = 7 Solving for variable 'n'. Reorder the terms: -35 + -7 + -2n + n2 = 7 + -7 Combine like terms: -35 + -7 = -42 -42 + -2n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -42 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -2n + 42 + n2 = 0 + 42 Reorder the terms: -42 + 42 + -2n + n2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -2n + n2 = 0 + 42 -2n + n2 = 0 + 42 Combine like terms: 0 + 42 = 42 -2n + n2 = 42 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 = 42 + 1 Reorder the terms: 1 + -2n + n2 = 42 + 1 Combine like terms: 42 + 1 = 43 1 + -2n + n2 = 43 Factor a perfect square on the left side: (n + -1)(n + -1) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (n + -1) equal to 6.557438524 and -6.557438524.Subproblem 1
n + -1 = 6.557438524 Simplifying n + -1 = 6.557438524 Reorder the terms: -1 + n = 6.557438524 Solving -1 + n = 6.557438524 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 = 6.557438524 + 1 Combine like terms: -1 + 1 = 0 0 + n = 6.557438524 + 1 n = 6.557438524 + 1 Combine like terms: 6.557438524 + 1 = 7.557438524 n = 7.557438524 Simplifying n = 7.557438524Subproblem 2
n + -1 = -6.557438524 Simplifying n + -1 = -6.557438524 Reorder the terms: -1 + n = -6.557438524 Solving -1 + n = -6.557438524 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 = -6.557438524 + 1 Combine like terms: -1 + 1 = 0 0 + n = -6.557438524 + 1 n = -6.557438524 + 1 Combine like terms: -6.557438524 + 1 = -5.557438524 n = -5.557438524 Simplifying n = -5.557438524Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.557438524, -5.557438524}
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