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Simplifying 9r2 + -45r + -133 = -7 Reorder the terms: -133 + -45r + 9r2 = -7 Solving -133 + -45r + 9r2 = -7 Solving for variable 'r'. Reorder the terms: -133 + 7 + -45r + 9r2 = -7 + 7 Combine like terms: -133 + 7 = -126 -126 + -45r + 9r2 = -7 + 7 Combine like terms: -7 + 7 = 0 -126 + -45r + 9r2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-14 + -5r + r2) = 0 Factor a trinomial. 9((-2 + -1r)(7 + -1r)) = 0 Ignore the factor 9.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 '(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 = {-2, 7}
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