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Simplifying 2r2 = 13r + 7 Reorder the terms: 2r2 = 7 + 13r Solving 2r2 = 7 + 13r Solving for variable 'r'. Reorder the terms: -7 + -13r + 2r2 = 7 + 13r + -7 + -13r Reorder the terms: -7 + -13r + 2r2 = 7 + -7 + 13r + -13r Combine like terms: 7 + -7 = 0 -7 + -13r + 2r2 = 0 + 13r + -13r -7 + -13r + 2r2 = 13r + -13r Combine like terms: 13r + -13r = 0 -7 + -13r + 2r2 = 0 Factor a trinomial. (-1 + -2r)(7 + -1r) = 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 '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Solution
r = {-0.5, 7}
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