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Simplifying 35n2 + -115n + -100 = 0 Reorder the terms: -100 + -115n + 35n2 = 0 Solving -100 + -115n + 35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -23n + 7n2) = 0 Factor a trinomial. 5((-5 + -7n)(4 + -1n)) = 0 Ignore the factor 5.Subproblem 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 '(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 = 4Solution
n = {-0.7142857143, 4}
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