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Simplifying 7n2 = -35 + 54n Solving 7n2 = -35 + 54n Solving for variable 'n'. Reorder the terms: 35 + -54n + 7n2 = -35 + 54n + 35 + -54n Reorder the terms: 35 + -54n + 7n2 = -35 + 35 + 54n + -54n Combine like terms: -35 + 35 = 0 35 + -54n + 7n2 = 0 + 54n + -54n 35 + -54n + 7n2 = 54n + -54n Combine like terms: 54n + -54n = 0 35 + -54n + 7n2 = 0 Factor a trinomial. (5 + -7n)(7 + -1n) = 0Subproblem 1
Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143Subproblem 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 = {0.7142857143, 7}
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