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Simplifying n2 + n = 110 Reorder the terms: n + n2 = 110 Solving n + n2 = 110 Solving for variable 'n'. Reorder the terms: -110 + n + n2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + n + n2 = 0 Factor a trinomial. (-11 + -1n)(10 + -1n) = 0Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve: Simplifying -11 + -1n = 0 Solving -11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1n = 0 + 11 -1n = 0 + 11 Combine like terms: 0 + 11 = 11 -1n = 11 Divide each side by '-1'. n = -11 Simplifying n = -11Subproblem 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 = {-11, 10}
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