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Simplifying n2 + -1n = 36 Reorder the terms: -1n + n2 = 36 Solving -1n + n2 = 36 Solving for variable 'n'. Reorder the terms: -36 + -1n + n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -1n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + -1n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1n + n2 = 0 + 36 -1n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1n + n2 = 36 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 36 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + -1n + n2 = 36.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (n + -0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
n + -0.5 = 6.020797289 Simplifying n + -0.5 = 6.020797289 Reorder the terms: -0.5 + n = 6.020797289 Solving -0.5 + n = 6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 6.020797289 + 0.5 n = 6.020797289 + 0.5 Combine like terms: 6.020797289 + 0.5 = 6.520797289 n = 6.520797289 Simplifying n = 6.520797289Subproblem 2
n + -0.5 = -6.020797289 Simplifying n + -0.5 = -6.020797289 Reorder the terms: -0.5 + n = -6.020797289 Solving -0.5 + n = -6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -6.020797289 + 0.5 n = -6.020797289 + 0.5 Combine like terms: -6.020797289 + 0.5 = -5.520797289 n = -5.520797289 Simplifying n = -5.520797289Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.520797289, -5.520797289}
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