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Simplifying 7r2 + -56r + 56 = 7 Reorder the terms: 56 + -56r + 7r2 = 7 Solving 56 + -56r + 7r2 = 7 Solving for variable 'r'. Reorder the terms: 56 + -7 + -56r + 7r2 = 7 + -7 Combine like terms: 56 + -7 = 49 49 + -56r + 7r2 = 7 + -7 Combine like terms: 7 + -7 = 0 49 + -56r + 7r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(7 + -8r + r2) = 0 Factor a trinomial. 7((1 + -1r)(7 + -1r)) = 0 Ignore the factor 7.Subproblem 1
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 = 1Subproblem 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 = {1, 7}
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