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Simplifying n2 + 12n + -36 = 0 Reorder the terms: -36 + 12n + n2 = 0 Solving -36 + 12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 12n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + 12n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12n + n2 = 0 + 36 12n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 12n + n2 = 36 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 = 36 + 36 Reorder the terms: 36 + 12n + n2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12n + n2 = 72 Factor a perfect square on the left side: (n + 6)(n + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (n + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
n + 6 = 8.485281374 Simplifying n + 6 = 8.485281374 Reorder the terms: 6 + n = 8.485281374 Solving 6 + n = 8.485281374 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 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + n = 8.485281374 + -6 n = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 n = 2.485281374 Simplifying n = 2.485281374Subproblem 2
n + 6 = -8.485281374 Simplifying n + 6 = -8.485281374 Reorder the terms: 6 + n = -8.485281374 Solving 6 + n = -8.485281374 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 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + n = -8.485281374 + -6 n = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 n = -14.485281374 Simplifying n = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.485281374, -14.485281374}
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