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Simplifying 8n2 + -17 = 8n Reorder the terms: -17 + 8n2 = 8n Solving -17 + 8n2 = 8n Solving for variable 'n'. Reorder the terms: -17 + -8n + 8n2 = 8n + -8n Combine like terms: 8n + -8n = 0 -17 + -8n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + -1n + n2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -1n + 2.125 + n2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -1n + n2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -1n + n2 = 0 + 2.125 -1n + n2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -1n + n2 = 2.125 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 2.125 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 2.125 + 0.25 Combine like terms: 2.125 + 0.25 = 2.375 0.25 + -1n + n2 = 2.375 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2.375 Calculate the square root of the right side: 1.541103501 Break this problem into two subproblems by setting (n + -0.5) equal to 1.541103501 and -1.541103501.Subproblem 1
n + -0.5 = 1.541103501 Simplifying n + -0.5 = 1.541103501 Reorder the terms: -0.5 + n = 1.541103501 Solving -0.5 + n = 1.541103501 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.541103501 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.541103501 + 0.5 n = 1.541103501 + 0.5 Combine like terms: 1.541103501 + 0.5 = 2.041103501 n = 2.041103501 Simplifying n = 2.041103501Subproblem 2
n + -0.5 = -1.541103501 Simplifying n + -0.5 = -1.541103501 Reorder the terms: -0.5 + n = -1.541103501 Solving -0.5 + n = -1.541103501 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.541103501 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.541103501 + 0.5 n = -1.541103501 + 0.5 Combine like terms: -1.541103501 + 0.5 = -1.041103501 n = -1.041103501 Simplifying n = -1.041103501Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.041103501, -1.041103501}
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