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Simplifying 10n2 + -42n + -38 = 2 Reorder the terms: -38 + -42n + 10n2 = 2 Solving -38 + -42n + 10n2 = 2 Solving for variable 'n'. Reorder the terms: -38 + -2 + -42n + 10n2 = 2 + -2 Combine like terms: -38 + -2 = -40 -40 + -42n + 10n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -40 + -42n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -21n + 5n2) = 0 Factor a trinomial. 2((-4 + -5n)(5 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {-0.8, 5}
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