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Simplifying 8n2 + -8n + -18 = 0 Reorder the terms: -18 + -8n + 8n2 = 0 Solving -18 + -8n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -4n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -4n + 4n2)' equal to zero and attempt to solve: Simplifying -9 + -4n + 4n2 = 0 Solving -9 + -4n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -1n + n2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1n + 2.25 + n2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1n + n2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1n + n2 = 0 + 2.25 -1n + n2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1n + n2 = 2.25 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 2.25 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 0.25 + -1n + n2 = 2.5 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (n + -0.5) equal to 1.58113883 and -1.58113883.Subproblem 1
n + -0.5 = 1.58113883 Simplifying n + -0.5 = 1.58113883 Reorder the terms: -0.5 + n = 1.58113883 Solving -0.5 + n = 1.58113883 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.58113883 + 0.5 n = 1.58113883 + 0.5 Combine like terms: 1.58113883 + 0.5 = 2.08113883 n = 2.08113883 Simplifying n = 2.08113883Subproblem 2
n + -0.5 = -1.58113883 Simplifying n + -0.5 = -1.58113883 Reorder the terms: -0.5 + n = -1.58113883 Solving -0.5 + n = -1.58113883 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.58113883 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.58113883 + 0.5 n = -1.58113883 + 0.5 Combine like terms: -1.58113883 + 0.5 = -1.08113883 n = -1.08113883 Simplifying n = -1.08113883Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.08113883, -1.08113883}Solution
n = {2.08113883, -1.08113883}
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