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Simplifying N2 + 6N + -41 = 7 Reorder the terms: -41 + 6N + N2 = 7 Solving -41 + 6N + N2 = 7 Solving for variable 'N'. Reorder the terms: -41 + -7 + 6N + N2 = 7 + -7 Combine like terms: -41 + -7 = -48 -48 + 6N + N2 = 7 + -7 Combine like terms: 7 + -7 = 0 -48 + 6N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 6N + 48 + N2 = 0 + 48 Reorder the terms: -48 + 48 + 6N + N2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 6N + N2 = 0 + 48 6N + N2 = 0 + 48 Combine like terms: 0 + 48 = 48 6N + N2 = 48 The N term is 6N. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6N + 9 + N2 = 48 + 9 Reorder the terms: 9 + 6N + N2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + 6N + N2 = 57 Factor a perfect square on the left side: (N + 3)(N + 3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (N + 3) equal to 7.549834435 and -7.549834435.Subproblem 1
N + 3 = 7.549834435 Simplifying N + 3 = 7.549834435 Reorder the terms: 3 + N = 7.549834435 Solving 3 + N = 7.549834435 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + N = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + N = 7.549834435 + -3 N = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 N = 4.549834435 Simplifying N = 4.549834435Subproblem 2
N + 3 = -7.549834435 Simplifying N + 3 = -7.549834435 Reorder the terms: 3 + N = -7.549834435 Solving 3 + N = -7.549834435 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + N = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + N = -7.549834435 + -3 N = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 N = -10.549834435 Simplifying N = -10.549834435Solution
The solution to the problem is based on the solutions from the subproblems. N = {4.549834435, -10.549834435}
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