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Simplifying 0 = r2 + 25r + 100 Reorder the terms: 0 = 100 + 25r + r2 Solving 0 = 100 + 25r + r2 Solving for variable 'r'. Combine like terms: 0 + -100 = -100 -100 + -25r + -1r2 = 100 + 25r + r2 + -100 + -25r + -1r2 Reorder the terms: -100 + -25r + -1r2 = 100 + -100 + 25r + -25r + r2 + -1r2 Combine like terms: 100 + -100 = 0 -100 + -25r + -1r2 = 0 + 25r + -25r + r2 + -1r2 -100 + -25r + -1r2 = 25r + -25r + r2 + -1r2 Combine like terms: 25r + -25r = 0 -100 + -25r + -1r2 = 0 + r2 + -1r2 -100 + -25r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -100 + -25r + -1r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 25r + r2) = 0 Factor a trinomial. -1((20 + r)(5 + r)) = 0 Ignore the factor -1.Subproblem 1
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 = -20Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Solution
r = {-20, -5}
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