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Simplifying 2n2 + 8n + -150 = 0 Reorder the terms: -150 + 8n + 2n2 = 0 Solving -150 + 8n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 4n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 4n + n2)' equal to zero and attempt to solve: Simplifying -75 + 4n + n2 = 0 Solving -75 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 4n + 75 + n2 = 0 + 75 Reorder the terms: -75 + 75 + 4n + n2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 4n + n2 = 0 + 75 4n + n2 = 0 + 75 Combine like terms: 0 + 75 = 75 4n + n2 = 75 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 = 75 + 4 Reorder the terms: 4 + 4n + n2 = 75 + 4 Combine like terms: 75 + 4 = 79 4 + 4n + n2 = 79 Factor a perfect square on the left side: (n + 2)(n + 2) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (n + 2) equal to 8.888194417 and -8.888194417.Subproblem 1
n + 2 = 8.888194417 Simplifying n + 2 = 8.888194417 Reorder the terms: 2 + n = 8.888194417 Solving 2 + n = 8.888194417 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 = 8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + n = 8.888194417 + -2 n = 8.888194417 + -2 Combine like terms: 8.888194417 + -2 = 6.888194417 n = 6.888194417 Simplifying n = 6.888194417Subproblem 2
n + 2 = -8.888194417 Simplifying n + 2 = -8.888194417 Reorder the terms: 2 + n = -8.888194417 Solving 2 + n = -8.888194417 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 = -8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + n = -8.888194417 + -2 n = -8.888194417 + -2 Combine like terms: -8.888194417 + -2 = -10.888194417 n = -10.888194417 Simplifying n = -10.888194417Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.888194417, -10.888194417}Solution
n = {6.888194417, -10.888194417}
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