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Simplifying n2 + 4n + -32 = 6 Reorder the terms: -32 + 4n + n2 = 6 Solving -32 + 4n + n2 = 6 Solving for variable 'n'. Reorder the terms: -32 + -6 + 4n + n2 = 6 + -6 Combine like terms: -32 + -6 = -38 -38 + 4n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -38 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 4n + 38 + n2 = 0 + 38 Reorder the terms: -38 + 38 + 4n + n2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 4n + n2 = 0 + 38 4n + n2 = 0 + 38 Combine like terms: 0 + 38 = 38 4n + n2 = 38 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 = 38 + 4 Reorder the terms: 4 + 4n + n2 = 38 + 4 Combine like terms: 38 + 4 = 42 4 + 4n + n2 = 42 Factor a perfect square on the left side: (n + 2)(n + 2) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (n + 2) equal to 6.480740698 and -6.480740698.Subproblem 1
n + 2 = 6.480740698 Simplifying n + 2 = 6.480740698 Reorder the terms: 2 + n = 6.480740698 Solving 2 + n = 6.480740698 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 = 6.480740698 + -2 Combine like terms: 2 + -2 = 0 0 + n = 6.480740698 + -2 n = 6.480740698 + -2 Combine like terms: 6.480740698 + -2 = 4.480740698 n = 4.480740698 Simplifying n = 4.480740698Subproblem 2
n + 2 = -6.480740698 Simplifying n + 2 = -6.480740698 Reorder the terms: 2 + n = -6.480740698 Solving 2 + n = -6.480740698 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 = -6.480740698 + -2 Combine like terms: 2 + -2 = 0 0 + n = -6.480740698 + -2 n = -6.480740698 + -2 Combine like terms: -6.480740698 + -2 = -8.480740698 n = -8.480740698 Simplifying n = -8.480740698Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.480740698, -8.480740698}
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