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Simplifying 8n2 + -12n + -2 = 0 Reorder the terms: -2 + -12n + 8n2 = 0 Solving -2 + -12n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -6n + 4n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6n + 4n2)' equal to zero and attempt to solve: Simplifying -1 + -6n + 4n2 = 0 Solving -1 + -6n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1.5n + n2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.5n + 0.25 + n2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.5n + n2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.5n + n2 = 0 + 0.25 -1.5n + n2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.5n + n2 = 0.25 The n term is -1.5n. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5n + 0.5625 + n2 = 0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5n + n2 = 0.25 + 0.5625 Combine like terms: 0.25 + 0.5625 = 0.8125 0.5625 + -1.5n + n2 = 0.8125 Factor a perfect square on the left side: (n + -0.75)(n + -0.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (n + -0.75) equal to 0.901387819 and -0.901387819.Subproblem 1
n + -0.75 = 0.901387819 Simplifying n + -0.75 = 0.901387819 Reorder the terms: -0.75 + n = 0.901387819 Solving -0.75 + n = 0.901387819 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = 0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = 0.901387819 + 0.75 n = 0.901387819 + 0.75 Combine like terms: 0.901387819 + 0.75 = 1.651387819 n = 1.651387819 Simplifying n = 1.651387819Subproblem 2
n + -0.75 = -0.901387819 Simplifying n + -0.75 = -0.901387819 Reorder the terms: -0.75 + n = -0.901387819 Solving -0.75 + n = -0.901387819 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + n = -0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + n = -0.901387819 + 0.75 n = -0.901387819 + 0.75 Combine like terms: -0.901387819 + 0.75 = -0.151387819 n = -0.151387819 Simplifying n = -0.151387819Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.651387819, -0.151387819}Solution
n = {1.651387819, -0.151387819}
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