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Simplifying -2n2 = -15n + -22 Reorder the terms: -2n2 = -22 + -15n Solving -2n2 = -22 + -15n Solving for variable 'n'. Reorder the terms: 22 + 15n + -2n2 = -22 + -15n + 22 + 15n Reorder the terms: 22 + 15n + -2n2 = -22 + 22 + -15n + 15n Combine like terms: -22 + 22 = 0 22 + 15n + -2n2 = 0 + -15n + 15n 22 + 15n + -2n2 = -15n + 15n Combine like terms: -15n + 15n = 0 22 + 15n + -2n2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11 + -7.5n + n2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -7.5n + 11 + n2 = 0 + 11 Reorder the terms: -11 + 11 + -7.5n + n2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -7.5n + n2 = 0 + 11 -7.5n + n2 = 0 + 11 Combine like terms: 0 + 11 = 11 -7.5n + n2 = 11 The n term is -7.5n. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5n + 14.0625 + n2 = 11 + 14.0625 Reorder the terms: 14.0625 + -7.5n + n2 = 11 + 14.0625 Combine like terms: 11 + 14.0625 = 25.0625 14.0625 + -7.5n + n2 = 25.0625 Factor a perfect square on the left side: (n + -3.75)(n + -3.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (n + -3.75) equal to 5.006246099 and -5.006246099.Subproblem 1
n + -3.75 = 5.006246099 Simplifying n + -3.75 = 5.006246099 Reorder the terms: -3.75 + n = 5.006246099 Solving -3.75 + n = 5.006246099 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + n = 5.006246099 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + n = 5.006246099 + 3.75 n = 5.006246099 + 3.75 Combine like terms: 5.006246099 + 3.75 = 8.756246099 n = 8.756246099 Simplifying n = 8.756246099Subproblem 2
n + -3.75 = -5.006246099 Simplifying n + -3.75 = -5.006246099 Reorder the terms: -3.75 + n = -5.006246099 Solving -3.75 + n = -5.006246099 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + n = -5.006246099 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + n = -5.006246099 + 3.75 n = -5.006246099 + 3.75 Combine like terms: -5.006246099 + 3.75 = -1.256246099 n = -1.256246099 Simplifying n = -1.256246099Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.756246099, -1.256246099}
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