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Simplifying 4n2 = 10n + 14 Reorder the terms: 4n2 = 14 + 10n Solving 4n2 = 14 + 10n Solving for variable 'n'. Reorder the terms: -14 + -10n + 4n2 = 14 + 10n + -14 + -10n Reorder the terms: -14 + -10n + 4n2 = 14 + -14 + 10n + -10n Combine like terms: 14 + -14 = 0 -14 + -10n + 4n2 = 0 + 10n + -10n -14 + -10n + 4n2 = 10n + -10n Combine like terms: 10n + -10n = 0 -14 + -10n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -5n + 2n2) = 0 Factor a trinomial. 2((-1 + -1n)(7 + -2n)) = 0 Ignore the factor 2.Subproblem 1
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 = -1Subproblem 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 = {-1, 3.5}
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