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Simplifying 8n2 + -36n + -28 = 0 Reorder the terms: -28 + -36n + 8n2 = 0 Solving -28 + -36n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + -9n + 2n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -9n + 2n2)' equal to zero and attempt to solve: Simplifying -7 + -9n + 2n2 = 0 Solving -7 + -9n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -4.5n + n2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -4.5n + 3.5 + n2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -4.5n + n2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -4.5n + n2 = 0 + 3.5 -4.5n + n2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -4.5n + n2 = 3.5 The n term is -4.5n. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5n + 5.0625 + n2 = 3.5 + 5.0625 Reorder the terms: 5.0625 + -4.5n + n2 = 3.5 + 5.0625 Combine like terms: 3.5 + 5.0625 = 8.5625 5.0625 + -4.5n + n2 = 8.5625 Factor a perfect square on the left side: (n + -2.25)(n + -2.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (n + -2.25) equal to 2.926174978 and -2.926174978.Subproblem 1
n + -2.25 = 2.926174978 Simplifying n + -2.25 = 2.926174978 Reorder the terms: -2.25 + n = 2.926174978 Solving -2.25 + n = 2.926174978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + n = 2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = 2.926174978 + 2.25 n = 2.926174978 + 2.25 Combine like terms: 2.926174978 + 2.25 = 5.176174978 n = 5.176174978 Simplifying n = 5.176174978Subproblem 2
n + -2.25 = -2.926174978 Simplifying n + -2.25 = -2.926174978 Reorder the terms: -2.25 + n = -2.926174978 Solving -2.25 + n = -2.926174978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + n = -2.926174978 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = -2.926174978 + 2.25 n = -2.926174978 + 2.25 Combine like terms: -2.926174978 + 2.25 = -0.676174978 n = -0.676174978 Simplifying n = -0.676174978Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.176174978, -0.676174978}Solution
n = {5.176174978, -0.676174978}
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