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Simplifying n2 + -8 = 3n Reorder the terms: -8 + n2 = 3n Solving -8 + n2 = 3n Solving for variable 'n'. Reorder the terms: -8 + -3n + n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -8 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -3n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -3n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n + n2 = 0 + 8 -3n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3n + n2 = 8 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 8 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3n + n2 = 10.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (n + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
n + -1.5 = 3.201562119 Simplifying n + -1.5 = 3.201562119 Reorder the terms: -1.5 + n = 3.201562119 Solving -1.5 + n = 3.201562119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 3.201562119 + 1.5 n = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 n = 4.701562119 Simplifying n = 4.701562119Subproblem 2
n + -1.5 = -3.201562119 Simplifying n + -1.5 = -3.201562119 Reorder the terms: -1.5 + n = -3.201562119 Solving -1.5 + n = -3.201562119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -3.201562119 + 1.5 n = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 n = -1.701562119 Simplifying n = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.701562119, -1.701562119}
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