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Simplifying 20n2 + -66n + -14 = 0 Reorder the terms: -14 + -66n + 20n2 = 0 Solving -14 + -66n + 20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -33n + 10n2) = 0 Factor a trinomial. 2((-1 + -5n)(7 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve: Simplifying -1 + -5n = 0 Solving -1 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5n = 0 + 1 -5n = 0 + 1 Combine like terms: 0 + 1 = 1 -5n = 1 Divide each side by '-5'. n = -0.2 Simplifying n = -0.2Subproblem 2
Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {-0.2, 3.5}
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