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Simplifying n2 + -19n + -290 = 0 Reorder the terms: -290 + -19n + n2 = 0 Solving -290 + -19n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (-10 + -1n)(29 + -1n) = 0Subproblem 1
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 = -10Subproblem 2
Set the factor '(29 + -1n)' equal to zero and attempt to solve: Simplifying 29 + -1n = 0 Solving 29 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -1n = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -1n = 0 + -29 -1n = 0 + -29 Combine like terms: 0 + -29 = -29 -1n = -29 Divide each side by '-1'. n = 29 Simplifying n = 29Solution
n = {-10, 29}
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