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Simplifying n2 + -13n + -22 = 0 Reorder the terms: -22 + -13n + n2 = 0 Solving -22 + -13n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -13n + 22 + n2 = 0 + 22 Reorder the terms: -22 + 22 + -13n + n2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -13n + n2 = 0 + 22 -13n + n2 = 0 + 22 Combine like terms: 0 + 22 = 22 -13n + n2 = 22 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 = 22 + 42.25 Reorder the terms: 42.25 + -13n + n2 = 22 + 42.25 Combine like terms: 22 + 42.25 = 64.25 42.25 + -13n + n2 = 64.25 Factor a perfect square on the left side: (n + -6.5)(n + -6.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (n + -6.5) equal to 8.015609771 and -8.015609771.Subproblem 1
n + -6.5 = 8.015609771 Simplifying n + -6.5 = 8.015609771 Reorder the terms: -6.5 + n = 8.015609771 Solving -6.5 + n = 8.015609771 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 = 8.015609771 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = 8.015609771 + 6.5 n = 8.015609771 + 6.5 Combine like terms: 8.015609771 + 6.5 = 14.515609771 n = 14.515609771 Simplifying n = 14.515609771Subproblem 2
n + -6.5 = -8.015609771 Simplifying n + -6.5 = -8.015609771 Reorder the terms: -6.5 + n = -8.015609771 Solving -6.5 + n = -8.015609771 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 = -8.015609771 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = -8.015609771 + 6.5 n = -8.015609771 + 6.5 Combine like terms: -8.015609771 + 6.5 = -1.515609771 n = -1.515609771 Simplifying n = -1.515609771Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.515609771, -1.515609771}
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