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Simplifying n(n) + -4n + 1 = 5 Multiply n * n n2 + -4n + 1 = 5 Reorder the terms: 1 + -4n + n2 = 5 Solving 1 + -4n + n2 = 5 Solving for variable 'n'. Reorder the terms: 1 + -5 + -4n + n2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + -4n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -4n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4n + n2 = 0 + 4 -4n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4n + n2 = 4 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 = 4 + 4 Reorder the terms: 4 + -4n + n2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4n + n2 = 8 Factor a perfect square on the left side: (n + -2)(n + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (n + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
n + -2 = 2.828427125 Simplifying n + -2 = 2.828427125 Reorder the terms: -2 + n = 2.828427125 Solving -2 + n = 2.828427125 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 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + n = 2.828427125 + 2 n = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 n = 4.828427125 Simplifying n = 4.828427125Subproblem 2
n + -2 = -2.828427125 Simplifying n + -2 = -2.828427125 Reorder the terms: -2 + n = -2.828427125 Solving -2 + n = -2.828427125 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 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + n = -2.828427125 + 2 n = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 n = -0.828427125 Simplifying n = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.828427125, -0.828427125}
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