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Simplifying 45 = 4r + r2 Solving 45 = 4r + r2 Solving for variable 'r'. Reorder the terms: 45 + -4r + -1r2 = 4r + -4r + r2 + -1r2 Combine like terms: 4r + -4r = 0 45 + -4r + -1r2 = 0 + r2 + -1r2 45 + -4r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 45 + -4r + -1r2 = 0 Factor a trinomial. (5 + -1r)(9 + r) = 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 '(9 + r)' equal to zero and attempt to solve: Simplifying 9 + r = 0 Solving 9 + r = 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 + r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + r = 0 + -9 r = 0 + -9 Combine like terms: 0 + -9 = -9 r = -9 Simplifying r = -9Solution
r = {5, -9}
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