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Simplifying 25n2 + -96n + 79 = -5n2 + 7 Reorder the terms: 79 + -96n + 25n2 = -5n2 + 7 Reorder the terms: 79 + -96n + 25n2 = 7 + -5n2 Solving 79 + -96n + 25n2 = 7 + -5n2 Solving for variable 'n'. Reorder the terms: 79 + -7 + -96n + 25n2 + 5n2 = 7 + -5n2 + -7 + 5n2 Combine like terms: 79 + -7 = 72 72 + -96n + 25n2 + 5n2 = 7 + -5n2 + -7 + 5n2 Combine like terms: 25n2 + 5n2 = 30n2 72 + -96n + 30n2 = 7 + -5n2 + -7 + 5n2 Reorder the terms: 72 + -96n + 30n2 = 7 + -7 + -5n2 + 5n2 Combine like terms: 7 + -7 = 0 72 + -96n + 30n2 = 0 + -5n2 + 5n2 72 + -96n + 30n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 72 + -96n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(12 + -16n + 5n2) = 0 Factor a trinomial. 6((6 + -5n)(2 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(6 + -5n)' equal to zero and attempt to solve: Simplifying 6 + -5n = 0 Solving 6 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5n = 0 + -6 -5n = 0 + -6 Combine like terms: 0 + -6 = -6 -5n = -6 Divide each side by '-5'. n = 1.2 Simplifying n = 1.2Subproblem 2
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 = 2Solution
n = {1.2, 2}
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