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Simplifying r + -1(6r * r) = -1 Multiply r * r r + -1(6r2) = -1 Remove parenthesis around (6r2) r + -1 * 6r2 = -1 Multiply -1 * 6 r + -6r2 = -1 Solving r + -6r2 = -1 Solving for variable 'r'. Reorder the terms: 1 + r + -6r2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + r + -6r2 = 0 Factor a trinomial. (1 + -2r)(1 + 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 '(1 + 3r)' equal to zero and attempt to solve: Simplifying 1 + 3r = 0 Solving 1 + 3r = 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 + 3r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3r = 0 + -1 3r = 0 + -1 Combine like terms: 0 + -1 = -1 3r = -1 Divide each side by '3'. r = -0.3333333333 Simplifying r = -0.3333333333Solution
r = {0.5, -0.3333333333}
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