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Simplifying n2 + -4n + -256 = 0 Reorder the terms: -256 + -4n + n2 = 0 Solving -256 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + -4n + 256 + n2 = 0 + 256 Reorder the terms: -256 + 256 + -4n + n2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -4n + n2 = 0 + 256 -4n + n2 = 0 + 256 Combine like terms: 0 + 256 = 256 -4n + n2 = 256 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 = 256 + 4 Reorder the terms: 4 + -4n + n2 = 256 + 4 Combine like terms: 256 + 4 = 260 4 + -4n + n2 = 260 Factor a perfect square on the left side: (n + -2)(n + -2) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (n + -2) equal to 16.124515497 and -16.124515497.Subproblem 1
n + -2 = 16.124515497 Simplifying n + -2 = 16.124515497 Reorder the terms: -2 + n = 16.124515497 Solving -2 + n = 16.124515497 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 = 16.124515497 + 2 Combine like terms: -2 + 2 = 0 0 + n = 16.124515497 + 2 n = 16.124515497 + 2 Combine like terms: 16.124515497 + 2 = 18.124515497 n = 18.124515497 Simplifying n = 18.124515497Subproblem 2
n + -2 = -16.124515497 Simplifying n + -2 = -16.124515497 Reorder the terms: -2 + n = -16.124515497 Solving -2 + n = -16.124515497 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 = -16.124515497 + 2 Combine like terms: -2 + 2 = 0 0 + n = -16.124515497 + 2 n = -16.124515497 + 2 Combine like terms: -16.124515497 + 2 = -14.124515497 n = -14.124515497 Simplifying n = -14.124515497Solution
The solution to the problem is based on the solutions from the subproblems. n = {18.124515497, -14.124515497}
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