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Simplifying 8n2 + -40n + -49 = 0 Reorder the terms: -49 + -40n + 8n2 = 0 Solving -49 + -40n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.125 + -5n + n2 = 0 Move the constant term to the right: Add '6.125' to each side of the equation. -6.125 + -5n + 6.125 + n2 = 0 + 6.125 Reorder the terms: -6.125 + 6.125 + -5n + n2 = 0 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + -5n + n2 = 0 + 6.125 -5n + n2 = 0 + 6.125 Combine like terms: 0 + 6.125 = 6.125 -5n + n2 = 6.125 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 6.125 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 6.125 + 6.25 Combine like terms: 6.125 + 6.25 = 12.375 6.25 + -5n + n2 = 12.375 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 12.375 Calculate the square root of the right side: 3.51781182 Break this problem into two subproblems by setting (n + -2.5) equal to 3.51781182 and -3.51781182.Subproblem 1
n + -2.5 = 3.51781182 Simplifying n + -2.5 = 3.51781182 Reorder the terms: -2.5 + n = 3.51781182 Solving -2.5 + n = 3.51781182 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 3.51781182 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 3.51781182 + 2.5 n = 3.51781182 + 2.5 Combine like terms: 3.51781182 + 2.5 = 6.01781182 n = 6.01781182 Simplifying n = 6.01781182Subproblem 2
n + -2.5 = -3.51781182 Simplifying n + -2.5 = -3.51781182 Reorder the terms: -2.5 + n = -3.51781182 Solving -2.5 + n = -3.51781182 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -3.51781182 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -3.51781182 + 2.5 n = -3.51781182 + 2.5 Combine like terms: -3.51781182 + 2.5 = -1.01781182 n = -1.01781182 Simplifying n = -1.01781182Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.01781182, -1.01781182}
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