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Simplifying 7n2 + -10n + -53 = -5 Reorder the terms: -53 + -10n + 7n2 = -5 Solving -53 + -10n + 7n2 = -5 Solving for variable 'n'. Reorder the terms: -53 + 5 + -10n + 7n2 = -5 + 5 Combine like terms: -53 + 5 = -48 -48 + -10n + 7n2 = -5 + 5 Combine like terms: -5 + 5 = 0 -48 + -10n + 7n2 = 0 Factor a trinomial. (-2 + -1n)(24 + -7n) = 0Subproblem 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 '(24 + -7n)' equal to zero and attempt to solve: Simplifying 24 + -7n = 0 Solving 24 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -7n = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -7n = 0 + -24 -7n = 0 + -24 Combine like terms: 0 + -24 = -24 -7n = -24 Divide each side by '-7'. n = 3.428571429 Simplifying n = 3.428571429Solution
n = {-2, 3.428571429}
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