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Simplifying 4n2 + 10n = 14 Reorder the terms: 10n + 4n2 = 14 Solving 10n + 4n2 = 14 Solving for variable 'n'. Reorder the terms: -14 + 10n + 4n2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 10n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 5n + 2n2) = 0 Factor a trinomial. 2((-7 + -2n)(1 + -1n)) = 0 Ignore the factor 2.Subproblem 1
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 = -3.5Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-3.5, 1}
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