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Simplifying 10r2 + -7r + -4 = 5r2 + -8r Reorder the terms: -4 + -7r + 10r2 = 5r2 + -8r Reorder the terms: -4 + -7r + 10r2 = -8r + 5r2 Solving -4 + -7r + 10r2 = -8r + 5r2 Solving for variable 'r'. Reorder the terms: -4 + -7r + 8r + 10r2 + -5r2 = -8r + 5r2 + 8r + -5r2 Combine like terms: -7r + 8r = 1r -4 + 1r + 10r2 + -5r2 = -8r + 5r2 + 8r + -5r2 Combine like terms: 10r2 + -5r2 = 5r2 -4 + 1r + 5r2 = -8r + 5r2 + 8r + -5r2 Reorder the terms: -4 + 1r + 5r2 = -8r + 8r + 5r2 + -5r2 Combine like terms: -8r + 8r = 0 -4 + 1r + 5r2 = 0 + 5r2 + -5r2 -4 + 1r + 5r2 = 5r2 + -5r2 Combine like terms: 5r2 + -5r2 = 0 -4 + 1r + 5r2 = 0 Factor a trinomial. (-1 + -1r)(4 + -5r) = 0Subproblem 1
Set the factor '(-1 + -1r)' equal to zero and attempt to solve: Simplifying -1 + -1r = 0 Solving -1 + -1r = 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 + -1r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1r = 0 + 1 -1r = 0 + 1 Combine like terms: 0 + 1 = 1 -1r = 1 Divide each side by '-1'. r = -1 Simplifying r = -1Subproblem 2
Set the factor '(4 + -5r)' equal to zero and attempt to solve: Simplifying 4 + -5r = 0 Solving 4 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5r = 0 + -4 -5r = 0 + -4 Combine like terms: 0 + -4 = -4 -5r = -4 Divide each side by '-5'. r = 0.8 Simplifying r = 0.8Solution
r = {-1, 0.8}
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