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Simplifying 2r2 + -40r + 190 = -2 Reorder the terms: 190 + -40r + 2r2 = -2 Solving 190 + -40r + 2r2 = -2 Solving for variable 'r'. Reorder the terms: 190 + 2 + -40r + 2r2 = -2 + 2 Combine like terms: 190 + 2 = 192 192 + -40r + 2r2 = -2 + 2 Combine like terms: -2 + 2 = 0 192 + -40r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(96 + -20r + r2) = 0 Factor a trinomial. 2((8 + -1r)(12 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve: Simplifying 12 + -1r = 0 Solving 12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1r = 0 + -12 -1r = 0 + -12 Combine like terms: 0 + -12 = -12 -1r = -12 Divide each side by '-1'. r = 12 Simplifying r = 12Solution
r = {8, 12}
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