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Simplifying 4n2 + -5n + -8 = 0 Reorder the terms: -8 + -5n + 4n2 = 0 Solving -8 + -5n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -1.25n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.25n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -1.25n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.25n + n2 = 0 + 2 -1.25n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.25n + n2 = 2 The n term is -1.25n. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25n + 0.390625 + n2 = 2 + 0.390625 Reorder the terms: 0.390625 + -1.25n + n2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + -1.25n + n2 = 2.390625 Factor a perfect square on the left side: (n + -0.625)(n + -0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (n + -0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
n + -0.625 = 1.54616461 Simplifying n + -0.625 = 1.54616461 Reorder the terms: -0.625 + n = 1.54616461 Solving -0.625 + n = 1.54616461 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + n = 1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + n = 1.54616461 + 0.625 n = 1.54616461 + 0.625 Combine like terms: 1.54616461 + 0.625 = 2.17116461 n = 2.17116461 Simplifying n = 2.17116461Subproblem 2
n + -0.625 = -1.54616461 Simplifying n + -0.625 = -1.54616461 Reorder the terms: -0.625 + n = -1.54616461 Solving -0.625 + n = -1.54616461 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + n = -1.54616461 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + n = -1.54616461 + 0.625 n = -1.54616461 + 0.625 Combine like terms: -1.54616461 + 0.625 = -0.92116461 n = -0.92116461 Simplifying n = -0.92116461Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.17116461, -0.92116461}
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