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Simplifying 5n2 = -14 + 37n Solving 5n2 = -14 + 37n Solving for variable 'n'. Reorder the terms: 14 + -37n + 5n2 = -14 + 37n + 14 + -37n Reorder the terms: 14 + -37n + 5n2 = -14 + 14 + 37n + -37n Combine like terms: -14 + 14 = 0 14 + -37n + 5n2 = 0 + 37n + -37n 14 + -37n + 5n2 = 37n + -37n Combine like terms: 37n + -37n = 0 14 + -37n + 5n2 = 0 Factor a trinomial. (2 + -5n)(7 + -1n) = 0Subproblem 1
Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 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 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Subproblem 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 = {0.4, 7}
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