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Simplifying 3n2 + 24n + -36 = 0 Reorder the terms: -36 + 24n + 3n2 = 0 Solving -36 + 24n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 8n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 8n + n2)' equal to zero and attempt to solve: Simplifying -12 + 8n + n2 = 0 Solving -12 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 8n + 12 + n2 = 0 + 12 Reorder the terms: -12 + 12 + 8n + n2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8n + n2 = 0 + 12 8n + n2 = 0 + 12 Combine like terms: 0 + 12 = 12 8n + n2 = 12 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = 12 + 16 Reorder the terms: 16 + 8n + n2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8n + n2 = 28 Factor a perfect square on the left side: (n + 4)(n + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (n + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
n + 4 = 5.291502622 Simplifying n + 4 = 5.291502622 Reorder the terms: 4 + n = 5.291502622 Solving 4 + n = 5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + n = 5.291502622 + -4 n = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 n = 1.291502622 Simplifying n = 1.291502622Subproblem 2
n + 4 = -5.291502622 Simplifying n + 4 = -5.291502622 Reorder the terms: 4 + n = -5.291502622 Solving 4 + n = -5.291502622 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + n = -5.291502622 + -4 n = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 n = -9.291502622 Simplifying n = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.291502622, -9.291502622}Solution
n = {1.291502622, -9.291502622}
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