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Simplifying n2 + -1n + -480 = 0 Reorder the terms: -480 + -1n + n2 = 0 Solving -480 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + -1n + 480 + n2 = 0 + 480 Reorder the terms: -480 + 480 + -1n + n2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + -1n + n2 = 0 + 480 -1n + n2 = 0 + 480 Combine like terms: 0 + 480 = 480 -1n + n2 = 480 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 = 480 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 480 + 0.25 Combine like terms: 480 + 0.25 = 480.25 0.25 + -1n + n2 = 480.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (n + -0.5) equal to 21.914607001 and -21.914607001.Subproblem 1
n + -0.5 = 21.914607001 Simplifying n + -0.5 = 21.914607001 Reorder the terms: -0.5 + n = 21.914607001 Solving -0.5 + n = 21.914607001 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 = 21.914607001 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 21.914607001 + 0.5 n = 21.914607001 + 0.5 Combine like terms: 21.914607001 + 0.5 = 22.414607001 n = 22.414607001 Simplifying n = 22.414607001Subproblem 2
n + -0.5 = -21.914607001 Simplifying n + -0.5 = -21.914607001 Reorder the terms: -0.5 + n = -21.914607001 Solving -0.5 + n = -21.914607001 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 = -21.914607001 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -21.914607001 + 0.5 n = -21.914607001 + 0.5 Combine like terms: -21.914607001 + 0.5 = -21.414607001 n = -21.414607001 Simplifying n = -21.414607001Solution
The solution to the problem is based on the solutions from the subproblems. n = {22.414607001, -21.414607001}
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