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Simplifying 6r2 + -7r = 5 Reorder the terms: -7r + 6r2 = 5 Solving -7r + 6r2 = 5 Solving for variable 'r'. Reorder the terms: -5 + -7r + 6r2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -7r + 6r2 = 0 Factor a trinomial. (-1 + -2r)(5 + -3r) = 0Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve: Simplifying -1 + -2r = 0 Solving -1 + -2r = 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 + -2r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2r = 0 + 1 -2r = 0 + 1 Combine like terms: 0 + 1 = 1 -2r = 1 Divide each side by '-2'. r = -0.5 Simplifying r = -0.5Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {-0.5, 1.666666667}
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