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Simplifying (5r2 + 25r + -250) = 0 Reorder the terms: (-250 + 25r + 5r2) = 0 Remove parenthesis around (-250 + 25r + 5r2) -250 + 25r + 5r2 = 0 Solving -250 + 25r + 5r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(-50 + 5r + r2) = 0 Factor a trinomial. 5((-10 + -1r)(5 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve: Simplifying -10 + -1r = 0 Solving -10 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1r = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1r = 0 + 10 -1r = 0 + 10 Combine like terms: 0 + 10 = 10 -1r = 10 Divide each side by '-1'. r = -10 Simplifying r = -10Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5Solution
r = {-10, 5}
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