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Simplifying 2n2 + 8n = 44 Reorder the terms: 8n + 2n2 = 44 Solving 8n + 2n2 = 44 Solving for variable 'n'. Reorder the terms: -44 + 8n + 2n2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + 8n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 4n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 4n + n2)' equal to zero and attempt to solve: Simplifying -22 + 4n + n2 = 0 Solving -22 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 4n + 22 + n2 = 0 + 22 Reorder the terms: -22 + 22 + 4n + n2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 4n + n2 = 0 + 22 4n + n2 = 0 + 22 Combine like terms: 0 + 22 = 22 4n + n2 = 22 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 = 22 + 4 Reorder the terms: 4 + 4n + n2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + 4n + n2 = 26 Factor a perfect square on the left side: (n + 2)(n + 2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (n + 2) equal to 5.099019514 and -5.099019514.Subproblem 1
n + 2 = 5.099019514 Simplifying n + 2 = 5.099019514 Reorder the terms: 2 + n = 5.099019514 Solving 2 + n = 5.099019514 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 = 5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + n = 5.099019514 + -2 n = 5.099019514 + -2 Combine like terms: 5.099019514 + -2 = 3.099019514 n = 3.099019514 Simplifying n = 3.099019514Subproblem 2
n + 2 = -5.099019514 Simplifying n + 2 = -5.099019514 Reorder the terms: 2 + n = -5.099019514 Solving 2 + n = -5.099019514 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 = -5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + n = -5.099019514 + -2 n = -5.099019514 + -2 Combine like terms: -5.099019514 + -2 = -7.099019514 n = -7.099019514 Simplifying n = -7.099019514Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.099019514, -7.099019514}Solution
n = {3.099019514, -7.099019514}
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