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Simplifying 4r2 = 5r + 9 Reorder the terms: 4r2 = 9 + 5r Solving 4r2 = 9 + 5r Solving for variable 'r'. Reorder the terms: -9 + -5r + 4r2 = 9 + 5r + -9 + -5r Reorder the terms: -9 + -5r + 4r2 = 9 + -9 + 5r + -5r Combine like terms: 9 + -9 = 0 -9 + -5r + 4r2 = 0 + 5r + -5r -9 + -5r + 4r2 = 5r + -5r Combine like terms: 5r + -5r = 0 -9 + -5r + 4r2 = 0 Factor a trinomial. (-1 + -1r)(9 + -4r) = 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 '(9 + -4r)' equal to zero and attempt to solve: Simplifying 9 + -4r = 0 Solving 9 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4r = 0 + -9 -4r = 0 + -9 Combine like terms: 0 + -9 = -9 -4r = -9 Divide each side by '-4'. r = 2.25 Simplifying r = 2.25Solution
r = {-1, 2.25}
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