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Simplifying 8r2 + 14r + -4 = 0 Reorder the terms: -4 + 14r + 8r2 = 0 Solving -4 + 14r + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 7r + 4r2) = 0 Factor a trinomial. 2((-2 + -1r)(1 + -4r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
Set the factor '(1 + -4r)' equal to zero and attempt to solve: Simplifying 1 + -4r = 0 Solving 1 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4r = 0 + -1 -4r = 0 + -1 Combine like terms: 0 + -1 = -1 -4r = -1 Divide each side by '-4'. r = 0.25 Simplifying r = 0.25Solution
r = {-2, 0.25}
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