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Simplifying -3 = n2 + -14n + 37 Reorder the terms: -3 = 37 + -14n + n2 Solving -3 = 37 + -14n + n2 Solving for variable 'n'. Combine like terms: -3 + -37 = -40 -40 + 14n + -1n2 = 37 + -14n + n2 + -37 + 14n + -1n2 Reorder the terms: -40 + 14n + -1n2 = 37 + -37 + -14n + 14n + n2 + -1n2 Combine like terms: 37 + -37 = 0 -40 + 14n + -1n2 = 0 + -14n + 14n + n2 + -1n2 -40 + 14n + -1n2 = -14n + 14n + n2 + -1n2 Combine like terms: -14n + 14n = 0 -40 + 14n + -1n2 = 0 + n2 + -1n2 -40 + 14n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -40 + 14n + -1n2 = 0 Factor a trinomial. (-10 + n)(4 + -1n) = 0Subproblem 1
Set the factor '(-10 + n)' equal to zero and attempt to solve: Simplifying -10 + n = 0 Solving -10 + n = 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 + n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + n = 0 + 10 n = 0 + 10 Combine like terms: 0 + 10 = 10 n = 10 Simplifying n = 10Subproblem 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 = {10, 4}
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