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Simplifying 0 = r2 + 15r + -100 Reorder the terms: 0 = -100 + 15r + r2 Solving 0 = -100 + 15r + r2 Solving for variable 'r'. Combine like terms: 0 + 100 = 100 100 + -15r + -1r2 = -100 + 15r + r2 + 100 + -15r + -1r2 Reorder the terms: 100 + -15r + -1r2 = -100 + 100 + 15r + -15r + r2 + -1r2 Combine like terms: -100 + 100 = 0 100 + -15r + -1r2 = 0 + 15r + -15r + r2 + -1r2 100 + -15r + -1r2 = 15r + -15r + r2 + -1r2 Combine like terms: 15r + -15r = 0 100 + -15r + -1r2 = 0 + r2 + -1r2 100 + -15r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 100 + -15r + -1r2 = 0 Factor a trinomial. (5 + -1r)(20 + 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 '(20 + r)' equal to zero and attempt to solve: Simplifying 20 + r = 0 Solving 20 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = 0 + -20 Combine like terms: 20 + -20 = 0 0 + r = 0 + -20 r = 0 + -20 Combine like terms: 0 + -20 = -20 r = -20 Simplifying r = -20Solution
r = {5, -20}
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