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Simplifying n2 + 12n = -17 Reorder the terms: 12n + n2 = -17 Solving 12n + n2 = -17 Solving for variable 'n'. Reorder the terms: 17 + 12n + n2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 12n + -17 + n2 = 0 + -17 Reorder the terms: 17 + -17 + 12n + n2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 12n + n2 = 0 + -17 12n + n2 = 0 + -17 Combine like terms: 0 + -17 = -17 12n + n2 = -17 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 = -17 + 36 Reorder the terms: 36 + 12n + n2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + 12n + n2 = 19 Factor a perfect square on the left side: (n + 6)(n + 6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + 6) equal to 4.358898944 and -4.358898944.Subproblem 1
n + 6 = 4.358898944 Simplifying n + 6 = 4.358898944 Reorder the terms: 6 + n = 4.358898944 Solving 6 + n = 4.358898944 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 = 4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + n = 4.358898944 + -6 n = 4.358898944 + -6 Combine like terms: 4.358898944 + -6 = -1.641101056 n = -1.641101056 Simplifying n = -1.641101056Subproblem 2
n + 6 = -4.358898944 Simplifying n + 6 = -4.358898944 Reorder the terms: 6 + n = -4.358898944 Solving 6 + n = -4.358898944 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 = -4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + n = -4.358898944 + -6 n = -4.358898944 + -6 Combine like terms: -4.358898944 + -6 = -10.358898944 n = -10.358898944 Simplifying n = -10.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.641101056, -10.358898944}
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