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Simplifying 7n2 + -77n + 196 = 0 Reorder the terms: 196 + -77n + 7n2 = 0 Solving 196 + -77n + 7n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7'. 7(28 + -11n + n2) = 0 Factor a trinomial. 7((4 + -1n)(7 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 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 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {4, 7}
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