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Simplifying n2 + -4n + -35 = 0 Reorder the terms: -35 + -4n + n2 = 0 Solving -35 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -4n + 35 + n2 = 0 + 35 Reorder the terms: -35 + 35 + -4n + n2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -4n + n2 = 0 + 35 -4n + n2 = 0 + 35 Combine like terms: 0 + 35 = 35 -4n + n2 = 35 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 35 + 4 Reorder the terms: 4 + -4n + n2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + -4n + n2 = 39 Factor a perfect square on the left side: (n + -2)(n + -2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (n + -2) equal to 6.244997998 and -6.244997998.Subproblem 1
n + -2 = 6.244997998 Simplifying n + -2 = 6.244997998 Reorder the terms: -2 + n = 6.244997998 Solving -2 + n = 6.244997998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + n = 6.244997998 + 2 n = 6.244997998 + 2 Combine like terms: 6.244997998 + 2 = 8.244997998 n = 8.244997998 Simplifying n = 8.244997998Subproblem 2
n + -2 = -6.244997998 Simplifying n + -2 = -6.244997998 Reorder the terms: -2 + n = -6.244997998 Solving -2 + n = -6.244997998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + n = -6.244997998 + 2 n = -6.244997998 + 2 Combine like terms: -6.244997998 + 2 = -4.244997998 n = -4.244997998 Simplifying n = -4.244997998Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.244997998, -4.244997998}
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