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Simplifying n2 + 20n + -51 = -7 Reorder the terms: -51 + 20n + n2 = -7 Solving -51 + 20n + n2 = -7 Solving for variable 'n'. Reorder the terms: -51 + 7 + 20n + n2 = -7 + 7 Combine like terms: -51 + 7 = -44 -44 + 20n + n2 = -7 + 7 Combine like terms: -7 + 7 = 0 -44 + 20n + n2 = 0 Factor a trinomial. (-22 + -1n)(2 + -1n) = 0Subproblem 1
Set the factor '(-22 + -1n)' equal to zero and attempt to solve: Simplifying -22 + -1n = 0 Solving -22 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -1n = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1n = 0 + 22 -1n = 0 + 22 Combine like terms: 0 + 22 = 22 -1n = 22 Divide each side by '-1'. n = -22 Simplifying n = -22Subproblem 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 = {-22, 2}
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