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Simplifying 45r2 + -210r + 245 = 0 Reorder the terms: 245 + -210r + 45r2 = 0 Solving 245 + -210r + 45r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(49 + -42r + 9r2) = 0 Factor a trinomial. 5((7 + -3r)(7 + -3r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -3r)' equal to zero and attempt to solve: Simplifying 7 + -3r = 0 Solving 7 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3r = 0 + -7 -3r = 0 + -7 Combine like terms: 0 + -7 = -7 -3r = -7 Divide each side by '-3'. r = 2.333333333 Simplifying r = 2.333333333Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve: Simplifying 7 + -3r = 0 Solving 7 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3r = 0 + -7 -3r = 0 + -7 Combine like terms: 0 + -7 = -7 -3r = -7 Divide each side by '-3'. r = 2.333333333 Simplifying r = 2.333333333Solution
r = {2.333333333, 2.333333333}
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