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Simplifying 7n2 = 48n + 7 Reorder the terms: 7n2 = 7 + 48n Solving 7n2 = 7 + 48n Solving for variable 'n'. Reorder the terms: -7 + -48n + 7n2 = 7 + 48n + -7 + -48n Reorder the terms: -7 + -48n + 7n2 = 7 + -7 + 48n + -48n Combine like terms: 7 + -7 = 0 -7 + -48n + 7n2 = 0 + 48n + -48n -7 + -48n + 7n2 = 48n + -48n Combine like terms: 48n + -48n = 0 -7 + -48n + 7n2 = 0 Factor a trinomial. (-1 + -7n)(7 + -1n) = 0Subproblem 1
Set the factor '(-1 + -7n)' equal to zero and attempt to solve: Simplifying -1 + -7n = 0 Solving -1 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -7n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7n = 0 + 1 -7n = 0 + 1 Combine like terms: 0 + 1 = 1 -7n = 1 Divide each side by '-7'. n = -0.1428571429 Simplifying n = -0.1428571429Subproblem 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 = {-0.1428571429, 7}
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