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Simplifying 0 = 2r2 + -2r + -40 Reorder the terms: 0 = -40 + -2r + 2r2 Solving 0 = -40 + -2r + 2r2 Solving for variable 'r'. Combine like terms: 0 + 40 = 40 40 + 2r + -2r2 = -40 + -2r + 2r2 + 40 + 2r + -2r2 Reorder the terms: 40 + 2r + -2r2 = -40 + 40 + -2r + 2r + 2r2 + -2r2 Combine like terms: -40 + 40 = 0 40 + 2r + -2r2 = 0 + -2r + 2r + 2r2 + -2r2 40 + 2r + -2r2 = -2r + 2r + 2r2 + -2r2 Combine like terms: -2r + 2r = 0 40 + 2r + -2r2 = 0 + 2r2 + -2r2 40 + 2r + -2r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 40 + 2r + -2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + r + -1r2) = 0 Factor a trinomial. 2((5 + -1r)(4 + r)) = 0 Ignore the factor 2.Subproblem 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 '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Solution
r = {5, -4}
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