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Simplifying 10n2 + -35 = -65n Reorder the terms: -35 + 10n2 = -65n Solving -35 + 10n2 = -65n Solving for variable 'n'. Reorder the terms: -35 + 65n + 10n2 = -65n + 65n Combine like terms: -65n + 65n = 0 -35 + 65n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-7 + 13n + 2n2) = 0 Factor a trinomial. 5((-7 + -1n)(1 + -2n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 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 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-7, 0.5}
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