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Simplifying n2 + -13n + -50 = 0 Reorder the terms: -50 + -13n + n2 = 0 Solving -50 + -13n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -13n + 50 + n2 = 0 + 50 Reorder the terms: -50 + 50 + -13n + n2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -13n + n2 = 0 + 50 -13n + n2 = 0 + 50 Combine like terms: 0 + 50 = 50 -13n + n2 = 50 The n term is -13n. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13n + 42.25 + n2 = 50 + 42.25 Reorder the terms: 42.25 + -13n + n2 = 50 + 42.25 Combine like terms: 50 + 42.25 = 92.25 42.25 + -13n + n2 = 92.25 Factor a perfect square on the left side: (n + -6.5)(n + -6.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (n + -6.5) equal to 9.604686356 and -9.604686356.Subproblem 1
n + -6.5 = 9.604686356 Simplifying n + -6.5 = 9.604686356 Reorder the terms: -6.5 + n = 9.604686356 Solving -6.5 + n = 9.604686356 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + n = 9.604686356 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = 9.604686356 + 6.5 n = 9.604686356 + 6.5 Combine like terms: 9.604686356 + 6.5 = 16.104686356 n = 16.104686356 Simplifying n = 16.104686356Subproblem 2
n + -6.5 = -9.604686356 Simplifying n + -6.5 = -9.604686356 Reorder the terms: -6.5 + n = -9.604686356 Solving -6.5 + n = -9.604686356 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + n = -9.604686356 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = -9.604686356 + 6.5 n = -9.604686356 + 6.5 Combine like terms: -9.604686356 + 6.5 = -3.104686356 n = -3.104686356 Simplifying n = -3.104686356Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.104686356, -3.104686356}
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