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Simplifying 2n2 + -2n + -510 = 0 Reorder the terms: -510 + -2n + 2n2 = 0 Solving -510 + -2n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-255 + -1n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-255 + -1n + n2)' equal to zero and attempt to solve: Simplifying -255 + -1n + n2 = 0 Solving -255 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + -1n + 255 + n2 = 0 + 255 Reorder the terms: -255 + 255 + -1n + n2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + -1n + n2 = 0 + 255 -1n + n2 = 0 + 255 Combine like terms: 0 + 255 = 255 -1n + n2 = 255 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 = 255 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 255 + 0.25 Combine like terms: 255 + 0.25 = 255.25 0.25 + -1n + n2 = 255.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 255.25 Calculate the square root of the right side: 15.976545309 Break this problem into two subproblems by setting (n + -0.5) equal to 15.976545309 and -15.976545309.Subproblem 1
n + -0.5 = 15.976545309 Simplifying n + -0.5 = 15.976545309 Reorder the terms: -0.5 + n = 15.976545309 Solving -0.5 + n = 15.976545309 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 = 15.976545309 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 15.976545309 + 0.5 n = 15.976545309 + 0.5 Combine like terms: 15.976545309 + 0.5 = 16.476545309 n = 16.476545309 Simplifying n = 16.476545309Subproblem 2
n + -0.5 = -15.976545309 Simplifying n + -0.5 = -15.976545309 Reorder the terms: -0.5 + n = -15.976545309 Solving -0.5 + n = -15.976545309 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 = -15.976545309 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -15.976545309 + 0.5 n = -15.976545309 + 0.5 Combine like terms: -15.976545309 + 0.5 = -15.476545309 n = -15.476545309 Simplifying n = -15.476545309Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.476545309, -15.476545309}Solution
n = {16.476545309, -15.476545309}
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