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Simplifying 5r2 + 38r + -24 = -2r2 Reorder the terms: -24 + 38r + 5r2 = -2r2 Solving -24 + 38r + 5r2 = -2r2 Solving for variable 'r'. Combine like terms: 5r2 + 2r2 = 7r2 -24 + 38r + 7r2 = -2r2 + 2r2 Combine like terms: -2r2 + 2r2 = 0 -24 + 38r + 7r2 = 0 Factor a trinomial. (-6 + -1r)(4 + -7r) = 0Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 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 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6Subproblem 2
Set the factor '(4 + -7r)' equal to zero and attempt to solve: Simplifying 4 + -7r = 0 Solving 4 + -7r = 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 + -7r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7r = 0 + -4 -7r = 0 + -4 Combine like terms: 0 + -4 = -4 -7r = -4 Divide each side by '-7'. r = 0.5714285714 Simplifying r = 0.5714285714Solution
r = {-6, 0.5714285714}
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