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Simplifying 4n2 + -10n = 36 Reorder the terms: -10n + 4n2 = 36 Solving -10n + 4n2 = 36 Solving for variable 'n'. Reorder the terms: -36 + -10n + 4n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -10n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -5n + 2n2) = 0 Factor a trinomial. 2((-2 + -1n)(9 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(9 + -2n)' equal to zero and attempt to solve: Simplifying 9 + -2n = 0 Solving 9 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2n = 0 + -9 -2n = 0 + -9 Combine like terms: 0 + -9 = -9 -2n = -9 Divide each side by '-2'. n = 4.5 Simplifying n = 4.5Solution
n = {-2, 4.5}
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