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Simplifying r(2r + -31) + 65 = 0 Reorder the terms: r(-31 + 2r) + 65 = 0 (-31 * r + 2r * r) + 65 = 0 (-31r + 2r2) + 65 = 0 Reorder the terms: 65 + -31r + 2r2 = 0 Solving 65 + -31r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + -2r)(13 + -1r) = 0Subproblem 1
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Subproblem 2
Set the factor '(13 + -1r)' equal to zero and attempt to solve: Simplifying 13 + -1r = 0 Solving 13 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1r = 0 + -13 -1r = 0 + -13 Combine like terms: 0 + -13 = -13 -1r = -13 Divide each side by '-1'. r = 13 Simplifying r = 13Solution
r = {2.5, 13}
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