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Simplifying 4r2 = 75 + -5r Solving 4r2 = 75 + -5r Solving for variable 'r'. Reorder the terms: -75 + 5r + 4r2 = 75 + -5r + -75 + 5r Reorder the terms: -75 + 5r + 4r2 = 75 + -75 + -5r + 5r Combine like terms: 75 + -75 = 0 -75 + 5r + 4r2 = 0 + -5r + 5r -75 + 5r + 4r2 = -5r + 5r Combine like terms: -5r + 5r = 0 -75 + 5r + 4r2 = 0 Factor a trinomial. (-5 + -1r)(15 + -4r) = 0Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 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 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 2
Set the factor '(15 + -4r)' equal to zero and attempt to solve: Simplifying 15 + -4r = 0 Solving 15 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4r = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4r = 0 + -15 -4r = 0 + -15 Combine like terms: 0 + -15 = -15 -4r = -15 Divide each side by '-4'. r = 3.75 Simplifying r = 3.75Solution
r = {-5, 3.75}
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