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Simplifying 7r2 + -14r + -61 = -5 Reorder the terms: -61 + -14r + 7r2 = -5 Solving -61 + -14r + 7r2 = -5 Solving for variable 'r'. Reorder the terms: -61 + 5 + -14r + 7r2 = -5 + 5 Combine like terms: -61 + 5 = -56 -56 + -14r + 7r2 = -5 + 5 Combine like terms: -5 + 5 = 0 -56 + -14r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + -2r + r2) = 0 Factor a trinomial. 7((-2 + -1r)(4 + -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 '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Solution
r = {-2, 4}
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