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Simplifying 14n2 + -114n + 112 = 0 Reorder the terms: 112 + -114n + 14n2 = 0 Solving 112 + -114n + 14n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -57n + 7n2) = 0 Factor a trinomial. 2((8 + -7n)(7 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -7n)' equal to zero and attempt to solve: Simplifying 8 + -7n = 0 Solving 8 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7n = 0 + -8 -7n = 0 + -8 Combine like terms: 0 + -8 = -8 -7n = -8 Divide each side by '-7'. n = 1.142857143 Simplifying n = 1.142857143Subproblem 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 = {1.142857143, 7}
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