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Simplifying n2 + 12n + -11 = -7 Reorder the terms: -11 + 12n + n2 = -7 Solving -11 + 12n + n2 = -7 Solving for variable 'n'. Reorder the terms: -11 + 7 + 12n + n2 = -7 + 7 Combine like terms: -11 + 7 = -4 -4 + 12n + n2 = -7 + 7 Combine like terms: -7 + 7 = 0 -4 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 12n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + 12n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 12n + n2 = 0 + 4 12n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 12n + n2 = 4 The n term is 12n. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12n + 36 + n2 = 4 + 36 Reorder the terms: 36 + 12n + n2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + 12n + n2 = 40 Factor a perfect square on the left side: (n + 6)(n + 6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (n + 6) equal to 6.32455532 and -6.32455532.Subproblem 1
n + 6 = 6.32455532 Simplifying n + 6 = 6.32455532 Reorder the terms: 6 + n = 6.32455532 Solving 6 + n = 6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + n = 6.32455532 + -6 n = 6.32455532 + -6 Combine like terms: 6.32455532 + -6 = 0.32455532 n = 0.32455532 Simplifying n = 0.32455532Subproblem 2
n + 6 = -6.32455532 Simplifying n + 6 = -6.32455532 Reorder the terms: 6 + n = -6.32455532 Solving 6 + n = -6.32455532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = -6.32455532 + -6 Combine like terms: 6 + -6 = 0 0 + n = -6.32455532 + -6 n = -6.32455532 + -6 Combine like terms: -6.32455532 + -6 = -12.32455532 n = -12.32455532 Simplifying n = -12.32455532Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.32455532, -12.32455532}
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