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Simplifying n2 + -4n + 4 = 40 Reorder the terms: 4 + -4n + n2 = 40 Solving 4 + -4n + n2 = 40 Solving for variable 'n'. Reorder the terms: 4 + -40 + -4n + n2 = 40 + -40 Combine like terms: 4 + -40 = -36 -36 + -4n + n2 = 40 + -40 Combine like terms: 40 + -40 = 0 -36 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -4n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + -4n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -4n + n2 = 0 + 36 -4n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 -4n + n2 = 36 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 = 36 + 4 Reorder the terms: 4 + -4n + n2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + -4n + n2 = 40 Factor a perfect square on the left side: (n + -2)(n + -2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (n + -2) equal to 6.32455532 and -6.32455532.Subproblem 1
n + -2 = 6.32455532 Simplifying n + -2 = 6.32455532 Reorder the terms: -2 + n = 6.32455532 Solving -2 + n = 6.32455532 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 = 6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + n = 6.32455532 + 2 n = 6.32455532 + 2 Combine like terms: 6.32455532 + 2 = 8.32455532 n = 8.32455532 Simplifying n = 8.32455532Subproblem 2
n + -2 = -6.32455532 Simplifying n + -2 = -6.32455532 Reorder the terms: -2 + n = -6.32455532 Solving -2 + n = -6.32455532 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 = -6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + n = -6.32455532 + 2 n = -6.32455532 + 2 Combine like terms: -6.32455532 + 2 = -4.32455532 n = -4.32455532 Simplifying n = -4.32455532Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.32455532, -4.32455532}
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