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Simplifying 6r2 = 84r + -294 Reorder the terms: 6r2 = -294 + 84r Solving 6r2 = -294 + 84r Solving for variable 'r'. Reorder the terms: 294 + -84r + 6r2 = -294 + 84r + 294 + -84r Reorder the terms: 294 + -84r + 6r2 = -294 + 294 + 84r + -84r Combine like terms: -294 + 294 = 0 294 + -84r + 6r2 = 0 + 84r + -84r 294 + -84r + 6r2 = 84r + -84r Combine like terms: 84r + -84r = 0 294 + -84r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(49 + -14r + r2) = 0 Factor a trinomial. 6((7 + -1r)(7 + -1r)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 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 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 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 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Solution
r = {7, 7}
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