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Simplifying 2r2 = 8 + -15r Solving 2r2 = 8 + -15r Solving for variable 'r'. Reorder the terms: -8 + 15r + 2r2 = 8 + -15r + -8 + 15r Reorder the terms: -8 + 15r + 2r2 = 8 + -8 + -15r + 15r Combine like terms: 8 + -8 = 0 -8 + 15r + 2r2 = 0 + -15r + 15r -8 + 15r + 2r2 = -15r + 15r Combine like terms: -15r + 15r = 0 -8 + 15r + 2r2 = 0 Factor a trinomial. (-8 + -1r)(1 + -2r) = 0Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve: Simplifying -8 + -1r = 0 Solving -8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1r = 0 + 8 -1r = 0 + 8 Combine like terms: 0 + 8 = 8 -1r = 8 Divide each side by '-1'. r = -8 Simplifying r = -8Subproblem 2
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 = 0.5Solution
r = {-8, 0.5}
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