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Simplifying 4n2 + -16n + -30 = 0 Reorder the terms: -30 + -16n + 4n2 = 0 Solving -30 + -16n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -8n + 2n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -8n + 2n2)' equal to zero and attempt to solve: Simplifying -15 + -8n + 2n2 = 0 Solving -15 + -8n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -4n + n2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -4n + 7.5 + n2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -4n + n2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -4n + n2 = 0 + 7.5 -4n + n2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -4n + n2 = 7.5 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 = 7.5 + 4 Reorder the terms: 4 + -4n + n2 = 7.5 + 4 Combine like terms: 7.5 + 4 = 11.5 4 + -4n + n2 = 11.5 Factor a perfect square on the left side: (n + -2)(n + -2) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (n + -2) equal to 3.391164992 and -3.391164992.Subproblem 1
n + -2 = 3.391164992 Simplifying n + -2 = 3.391164992 Reorder the terms: -2 + n = 3.391164992 Solving -2 + n = 3.391164992 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 = 3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + n = 3.391164992 + 2 n = 3.391164992 + 2 Combine like terms: 3.391164992 + 2 = 5.391164992 n = 5.391164992 Simplifying n = 5.391164992Subproblem 2
n + -2 = -3.391164992 Simplifying n + -2 = -3.391164992 Reorder the terms: -2 + n = -3.391164992 Solving -2 + n = -3.391164992 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 = -3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + n = -3.391164992 + 2 n = -3.391164992 + 2 Combine like terms: -3.391164992 + 2 = -1.391164992 n = -1.391164992 Simplifying n = -1.391164992Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.391164992, -1.391164992}Solution
n = {5.391164992, -1.391164992}
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