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Simplifying 7r2 = 70r + -175 Reorder the terms: 7r2 = -175 + 70r Solving 7r2 = -175 + 70r Solving for variable 'r'. Reorder the terms: 175 + -70r + 7r2 = -175 + 70r + 175 + -70r Reorder the terms: 175 + -70r + 7r2 = -175 + 175 + 70r + -70r Combine like terms: -175 + 175 = 0 175 + -70r + 7r2 = 0 + 70r + -70r 175 + -70r + 7r2 = 70r + -70r Combine like terms: 70r + -70r = 0 175 + -70r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(25 + -10r + r2) = 0 Factor a trinomial. 7((5 + -1r)(5 + -1r)) = 0 Ignore the factor 7.Subproblem 1
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 = 5Subproblem 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 = {5, 5}
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