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Simplifying 5r2 = 10r + 75 Reorder the terms: 5r2 = 75 + 10r Solving 5r2 = 75 + 10r Solving for variable 'r'. Reorder the terms: -75 + -10r + 5r2 = 75 + 10r + -75 + -10r Reorder the terms: -75 + -10r + 5r2 = 75 + -75 + 10r + -10r Combine like terms: 75 + -75 = 0 -75 + -10r + 5r2 = 0 + 10r + -10r -75 + -10r + 5r2 = 10r + -10r Combine like terms: 10r + -10r = 0 -75 + -10r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + -2r + r2) = 0 Factor a trinomial. 5((-3 + -1r)(5 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 2
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 = 5Solution
r = {-3, 5}
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