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Simplifying 49n2 = 56n + 84 Reorder the terms: 49n2 = 84 + 56n Solving 49n2 = 84 + 56n Solving for variable 'n'. Reorder the terms: -84 + -56n + 49n2 = 84 + 56n + -84 + -56n Reorder the terms: -84 + -56n + 49n2 = 84 + -84 + 56n + -56n Combine like terms: 84 + -84 = 0 -84 + -56n + 49n2 = 0 + 56n + -56n -84 + -56n + 49n2 = 56n + -56n Combine like terms: 56n + -56n = 0 -84 + -56n + 49n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-12 + -8n + 7n2) = 0 Factor a trinomial. 7((-6 + -7n)(2 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-6 + -7n)' equal to zero and attempt to solve: Simplifying -6 + -7n = 0 Solving -6 + -7n = 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 + -7n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7n = 0 + 6 -7n = 0 + 6 Combine like terms: 0 + 6 = 6 -7n = 6 Divide each side by '-7'. n = -0.8571428571 Simplifying n = -0.8571428571Subproblem 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 = {-0.8571428571, 2}
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