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Simplifying 8n2 + -52n + -58 = 0 Reorder the terms: -58 + -52n + 8n2 = 0 Solving -58 + -52n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -26n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -26n + 4n2)' equal to zero and attempt to solve: Simplifying -29 + -26n + 4n2 = 0 Solving -29 + -26n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -6.5n + n2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -6.5n + 7.25 + n2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -6.5n + n2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -6.5n + n2 = 0 + 7.25 -6.5n + n2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -6.5n + n2 = 7.25 The n term is -6.5n. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5n + 10.5625 + n2 = 7.25 + 10.5625 Reorder the terms: 10.5625 + -6.5n + n2 = 7.25 + 10.5625 Combine like terms: 7.25 + 10.5625 = 17.8125 10.5625 + -6.5n + n2 = 17.8125 Factor a perfect square on the left side: (n + -3.25)(n + -3.25) = 17.8125 Calculate the square root of the right side: 4.220485754 Break this problem into two subproblems by setting (n + -3.25) equal to 4.220485754 and -4.220485754.Subproblem 1
n + -3.25 = 4.220485754 Simplifying n + -3.25 = 4.220485754 Reorder the terms: -3.25 + n = 4.220485754 Solving -3.25 + n = 4.220485754 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = 4.220485754 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 4.220485754 + 3.25 n = 4.220485754 + 3.25 Combine like terms: 4.220485754 + 3.25 = 7.470485754 n = 7.470485754 Simplifying n = 7.470485754Subproblem 2
n + -3.25 = -4.220485754 Simplifying n + -3.25 = -4.220485754 Reorder the terms: -3.25 + n = -4.220485754 Solving -3.25 + n = -4.220485754 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = -4.220485754 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -4.220485754 + 3.25 n = -4.220485754 + 3.25 Combine like terms: -4.220485754 + 3.25 = -0.970485754 n = -0.970485754 Simplifying n = -0.970485754Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.470485754, -0.970485754}Solution
n = {7.470485754, -0.970485754}
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