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Simplifying 15n2 + -24n + -9 = 0 Reorder the terms: -9 + -24n + 15n2 = 0 Solving -9 + -24n + 15n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -8n + 5n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -8n + 5n2)' equal to zero and attempt to solve: Simplifying -3 + -8n + 5n2 = 0 Solving -3 + -8n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.6n + n2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.6n + 0.6 + n2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.6n + n2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.6n + n2 = 0 + 0.6 -1.6n + n2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.6n + n2 = 0.6 The n term is -1.6n. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6n + 0.64 + n2 = 0.6 + 0.64 Reorder the terms: 0.64 + -1.6n + n2 = 0.6 + 0.64 Combine like terms: 0.6 + 0.64 = 1.24 0.64 + -1.6n + n2 = 1.24 Factor a perfect square on the left side: (n + -0.8)(n + -0.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (n + -0.8) equal to 1.113552873 and -1.113552873.Subproblem 1
n + -0.8 = 1.113552873 Simplifying n + -0.8 = 1.113552873 Reorder the terms: -0.8 + n = 1.113552873 Solving -0.8 + n = 1.113552873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + n = 1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = 1.113552873 + 0.8 n = 1.113552873 + 0.8 Combine like terms: 1.113552873 + 0.8 = 1.913552873 n = 1.913552873 Simplifying n = 1.913552873Subproblem 2
n + -0.8 = -1.113552873 Simplifying n + -0.8 = -1.113552873 Reorder the terms: -0.8 + n = -1.113552873 Solving -0.8 + n = -1.113552873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + n = -1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = -1.113552873 + 0.8 n = -1.113552873 + 0.8 Combine like terms: -1.113552873 + 0.8 = -0.313552873 n = -0.313552873 Simplifying n = -0.313552873Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.913552873, -0.313552873}Solution
n = {1.913552873, -0.313552873}
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