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Simplifying 7r2 + 7r = 14 Reorder the terms: 7r + 7r2 = 14 Solving 7r + 7r2 = 14 Solving for variable 'r'. Reorder the terms: -14 + 7r + 7r2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 7r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + r + r2) = 0 Factor a trinomial. 7((-2 + -1r)(1 + -1r)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {-2, 1}
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