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Simplifying r2 = 10r + 75 Reorder the terms: r2 = 75 + 10r Solving r2 = 75 + 10r Solving for variable 'r'. Reorder the terms: -75 + -10r + r2 = 75 + 10r + -75 + -10r Reorder the terms: -75 + -10r + r2 = 75 + -75 + 10r + -10r Combine like terms: 75 + -75 = 0 -75 + -10r + r2 = 0 + 10r + -10r -75 + -10r + r2 = 10r + -10r Combine like terms: 10r + -10r = 0 -75 + -10r + r2 = 0 Factor a trinomial. (-5 + -1r)(15 + -1r) = 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 + -1r)' equal to zero and attempt to solve: Simplifying 15 + -1r = 0 Solving 15 + -1r = 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 + -1r = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1r = 0 + -15 -1r = 0 + -15 Combine like terms: 0 + -15 = -15 -1r = -15 Divide each side by '-1'. r = 15 Simplifying r = 15Solution
r = {-5, 15}
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