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Simplifying -48 + -8n = -2n2 Solving -48 + -8n = -2n2 Solving for variable 'n'. Combine like terms: -2n2 + 2n2 = 0 -48 + -8n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -4n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -4n + n2)' equal to zero and attempt to solve: Simplifying -24 + -4n + n2 = 0 Solving -24 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -4n + 24 + n2 = 0 + 24 Reorder the terms: -24 + 24 + -4n + n2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4n + n2 = 0 + 24 -4n + n2 = 0 + 24 Combine like terms: 0 + 24 = 24 -4n + n2 = 24 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 24 + 4 Reorder the terms: 4 + -4n + n2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + -4n + n2 = 28 Factor a perfect square on the left side: (n + -2)(n + -2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (n + -2) equal to 5.291502622 and -5.291502622.Subproblem 1
n + -2 = 5.291502622 Simplifying n + -2 = 5.291502622 Reorder the terms: -2 + n = 5.291502622 Solving -2 + n = 5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + n = 5.291502622 + 2 n = 5.291502622 + 2 Combine like terms: 5.291502622 + 2 = 7.291502622 n = 7.291502622 Simplifying n = 7.291502622Subproblem 2
n + -2 = -5.291502622 Simplifying n + -2 = -5.291502622 Reorder the terms: -2 + n = -5.291502622 Solving -2 + n = -5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + n = -5.291502622 + 2 n = -5.291502622 + 2 Combine like terms: -5.291502622 + 2 = -3.291502622 n = -3.291502622 Simplifying n = -3.291502622Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.291502622, -3.291502622}Solution
n = {7.291502622, -3.291502622}
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