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Simplifying r2 + -1r = 21 + 3r Reorder the terms: -1r + r2 = 21 + 3r Solving -1r + r2 = 21 + 3r Solving for variable 'r'. Reorder the terms: -21 + -1r + -3r + r2 = 21 + 3r + -21 + -3r Combine like terms: -1r + -3r = -4r -21 + -4r + r2 = 21 + 3r + -21 + -3r Reorder the terms: -21 + -4r + r2 = 21 + -21 + 3r + -3r Combine like terms: 21 + -21 = 0 -21 + -4r + r2 = 0 + 3r + -3r -21 + -4r + r2 = 3r + -3r Combine like terms: 3r + -3r = 0 -21 + -4r + r2 = 0 Factor a trinomial. (-3 + -1r)(7 + -1r) = 0Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 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 = {-3, 7}
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