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Simplifying n2 + -14n = -40 Reorder the terms: -14n + n2 = -40 Solving -14n + n2 = -40 Solving for variable 'n'. Reorder the terms: 40 + -14n + n2 = -40 + 40 Combine like terms: -40 + 40 = 0 40 + -14n + n2 = 0 Factor a trinomial. (4 + -1n)(10 + -1n) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Solution
n = {4, 10}
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