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Simplifying 2n2 + -2n + -131070 = 0 Reorder the terms: -131070 + -2n + 2n2 = 0 Solving -131070 + -2n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-65535 + -1n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65535 + -1n + n2)' equal to zero and attempt to solve: Simplifying -65535 + -1n + n2 = 0 Solving -65535 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '65535' to each side of the equation. -65535 + -1n + 65535 + n2 = 0 + 65535 Reorder the terms: -65535 + 65535 + -1n + n2 = 0 + 65535 Combine like terms: -65535 + 65535 = 0 0 + -1n + n2 = 0 + 65535 -1n + n2 = 0 + 65535 Combine like terms: 0 + 65535 = 65535 -1n + n2 = 65535 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 = 65535 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 65535 + 0.25 Combine like terms: 65535 + 0.25 = 65535.25 0.25 + -1n + n2 = 65535.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 65535.25 Calculate the square root of the right side: 255.998535152 Break this problem into two subproblems by setting (n + -0.5) equal to 255.998535152 and -255.998535152.Subproblem 1
n + -0.5 = 255.998535152 Simplifying n + -0.5 = 255.998535152 Reorder the terms: -0.5 + n = 255.998535152 Solving -0.5 + n = 255.998535152 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 = 255.998535152 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 255.998535152 + 0.5 n = 255.998535152 + 0.5 Combine like terms: 255.998535152 + 0.5 = 256.498535152 n = 256.498535152 Simplifying n = 256.498535152Subproblem 2
n + -0.5 = -255.998535152 Simplifying n + -0.5 = -255.998535152 Reorder the terms: -0.5 + n = -255.998535152 Solving -0.5 + n = -255.998535152 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 = -255.998535152 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -255.998535152 + 0.5 n = -255.998535152 + 0.5 Combine like terms: -255.998535152 + 0.5 = -255.498535152 n = -255.498535152 Simplifying n = -255.498535152Solution
The solution to the problem is based on the solutions from the subproblems. n = {256.498535152, -255.498535152}Solution
n = {256.498535152, -255.498535152}
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