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Simplifying 7r2 = -22r + 24 Reorder the terms: 7r2 = 24 + -22r Solving 7r2 = 24 + -22r Solving for variable 'r'. Reorder the terms: -24 + 22r + 7r2 = 24 + -22r + -24 + 22r Reorder the terms: -24 + 22r + 7r2 = 24 + -24 + -22r + 22r Combine like terms: 24 + -24 = 0 -24 + 22r + 7r2 = 0 + -22r + 22r -24 + 22r + 7r2 = -22r + 22r Combine like terms: -22r + 22r = 0 -24 + 22r + 7r2 = 0 Factor a trinomial. (-4 + -1r)(6 + -7r) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(6 + -7r)' equal to zero and attempt to solve: Simplifying 6 + -7r = 0 Solving 6 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7r = 0 + -6 -7r = 0 + -6 Combine like terms: 0 + -6 = -6 -7r = -6 Divide each side by '-7'. r = 0.8571428571 Simplifying r = 0.8571428571Solution
r = {-4, 0.8571428571}
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