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Simplifying n2 + 4n + -18 = 0 Reorder the terms: -18 + 4n + n2 = 0 Solving -18 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 4n + 18 + n2 = 0 + 18 Reorder the terms: -18 + 18 + 4n + n2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 4n + n2 = 0 + 18 4n + n2 = 0 + 18 Combine like terms: 0 + 18 = 18 4n + n2 = 18 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 = 18 + 4 Reorder the terms: 4 + 4n + n2 = 18 + 4 Combine like terms: 18 + 4 = 22 4 + 4n + n2 = 22 Factor a perfect square on the left side: (n + 2)(n + 2) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (n + 2) equal to 4.69041576 and -4.69041576.Subproblem 1
n + 2 = 4.69041576 Simplifying n + 2 = 4.69041576 Reorder the terms: 2 + n = 4.69041576 Solving 2 + n = 4.69041576 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 = 4.69041576 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.69041576 + -2 n = 4.69041576 + -2 Combine like terms: 4.69041576 + -2 = 2.69041576 n = 2.69041576 Simplifying n = 2.69041576Subproblem 2
n + 2 = -4.69041576 Simplifying n + 2 = -4.69041576 Reorder the terms: 2 + n = -4.69041576 Solving 2 + n = -4.69041576 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 = -4.69041576 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.69041576 + -2 n = -4.69041576 + -2 Combine like terms: -4.69041576 + -2 = -6.69041576 n = -6.69041576 Simplifying n = -6.69041576Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.69041576, -6.69041576}
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