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Simplifying 2n2 + 4n + -12 = 0 Reorder the terms: -12 + 4n + 2n2 = 0 Solving -12 + 4n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 2n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 2n + n2)' equal to zero and attempt to solve: Simplifying -6 + 2n + n2 = 0 Solving -6 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + 2n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2n + n2 = 0 + 6 2n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 2n + n2 = 6 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 6 + 1 Reorder the terms: 1 + 2n + n2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2n + n2 = 7 Factor a perfect square on the left side: (n + 1)(n + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (n + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
n + 1 = 2.645751311 Simplifying n + 1 = 2.645751311 Reorder the terms: 1 + n = 2.645751311 Solving 1 + n = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.645751311 + -1 n = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 n = 1.645751311 Simplifying n = 1.645751311Subproblem 2
n + 1 = -2.645751311 Simplifying n + 1 = -2.645751311 Reorder the terms: 1 + n = -2.645751311 Solving 1 + n = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.645751311 + -1 n = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 n = -3.645751311 Simplifying n = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.645751311, -3.645751311}Solution
n = {1.645751311, -3.645751311}
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