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Simplifying 2n2 + 24n + -600 = 0 Reorder the terms: -600 + 24n + 2n2 = 0 Solving -600 + 24n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-300 + 12n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-300 + 12n + n2)' equal to zero and attempt to solve: Simplifying -300 + 12n + n2 = 0 Solving -300 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 12n + 300 + n2 = 0 + 300 Reorder the terms: -300 + 300 + 12n + n2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 12n + n2 = 0 + 300 12n + n2 = 0 + 300 Combine like terms: 0 + 300 = 300 12n + n2 = 300 The n term is 12n. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12n + 36 + n2 = 300 + 36 Reorder the terms: 36 + 12n + n2 = 300 + 36 Combine like terms: 300 + 36 = 336 36 + 12n + n2 = 336 Factor a perfect square on the left side: (n + 6)(n + 6) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (n + 6) equal to 18.33030278 and -18.33030278.Subproblem 1
n + 6 = 18.33030278 Simplifying n + 6 = 18.33030278 Reorder the terms: 6 + n = 18.33030278 Solving 6 + n = 18.33030278 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 18.33030278 + -6 Combine like terms: 6 + -6 = 0 0 + n = 18.33030278 + -6 n = 18.33030278 + -6 Combine like terms: 18.33030278 + -6 = 12.33030278 n = 12.33030278 Simplifying n = 12.33030278Subproblem 2
n + 6 = -18.33030278 Simplifying n + 6 = -18.33030278 Reorder the terms: 6 + n = -18.33030278 Solving 6 + n = -18.33030278 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = -18.33030278 + -6 Combine like terms: 6 + -6 = 0 0 + n = -18.33030278 + -6 n = -18.33030278 + -6 Combine like terms: -18.33030278 + -6 = -24.33030278 n = -24.33030278 Simplifying n = -24.33030278Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.33030278, -24.33030278}Solution
n = {12.33030278, -24.33030278}
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