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Simplifying n2 + 4n + -76 = 0 Reorder the terms: -76 + 4n + n2 = 0 Solving -76 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 4n + 76 + n2 = 0 + 76 Reorder the terms: -76 + 76 + 4n + n2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 4n + n2 = 0 + 76 4n + n2 = 0 + 76 Combine like terms: 0 + 76 = 76 4n + n2 = 76 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 = 76 + 4 Reorder the terms: 4 + 4n + n2 = 76 + 4 Combine like terms: 76 + 4 = 80 4 + 4n + n2 = 80 Factor a perfect square on the left side: (n + 2)(n + 2) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (n + 2) equal to 8.94427191 and -8.94427191.Subproblem 1
n + 2 = 8.94427191 Simplifying n + 2 = 8.94427191 Reorder the terms: 2 + n = 8.94427191 Solving 2 + n = 8.94427191 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 = 8.94427191 + -2 Combine like terms: 2 + -2 = 0 0 + n = 8.94427191 + -2 n = 8.94427191 + -2 Combine like terms: 8.94427191 + -2 = 6.94427191 n = 6.94427191 Simplifying n = 6.94427191Subproblem 2
n + 2 = -8.94427191 Simplifying n + 2 = -8.94427191 Reorder the terms: 2 + n = -8.94427191 Solving 2 + n = -8.94427191 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 = -8.94427191 + -2 Combine like terms: 2 + -2 = 0 0 + n = -8.94427191 + -2 n = -8.94427191 + -2 Combine like terms: -8.94427191 + -2 = -10.94427191 n = -10.94427191 Simplifying n = -10.94427191Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.94427191, -10.94427191}
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