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Simplifying n2 + 4n + -43 = 0 Reorder the terms: -43 + 4n + n2 = 0 Solving -43 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 4n + 43 + n2 = 0 + 43 Reorder the terms: -43 + 43 + 4n + n2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 4n + n2 = 0 + 43 4n + n2 = 0 + 43 Combine like terms: 0 + 43 = 43 4n + n2 = 43 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 = 43 + 4 Reorder the terms: 4 + 4n + n2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + 4n + n2 = 47 Factor a perfect square on the left side: (n + 2)(n + 2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (n + 2) equal to 6.8556546 and -6.8556546.Subproblem 1
n + 2 = 6.8556546 Simplifying n + 2 = 6.8556546 Reorder the terms: 2 + n = 6.8556546 Solving 2 + n = 6.8556546 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 = 6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + n = 6.8556546 + -2 n = 6.8556546 + -2 Combine like terms: 6.8556546 + -2 = 4.8556546 n = 4.8556546 Simplifying n = 4.8556546Subproblem 2
n + 2 = -6.8556546 Simplifying n + 2 = -6.8556546 Reorder the terms: 2 + n = -6.8556546 Solving 2 + n = -6.8556546 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 = -6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + n = -6.8556546 + -2 n = -6.8556546 + -2 Combine like terms: -6.8556546 + -2 = -8.8556546 n = -8.8556546 Simplifying n = -8.8556546Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.8556546, -8.8556546}
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