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Simplifying 14r2 + -43r + 20 = 0 Reorder the terms: 20 + -43r + 14r2 = 0 Solving 20 + -43r + 14r2 = 0 Solving for variable 'r'. Factor a trinomial. (4 + -7r)(5 + -2r) = 0Subproblem 1
Set the factor '(4 + -7r)' equal to zero and attempt to solve: Simplifying 4 + -7r = 0 Solving 4 + -7r = 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 + -7r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7r = 0 + -4 -7r = 0 + -4 Combine like terms: 0 + -4 = -4 -7r = -4 Divide each side by '-7'. r = 0.5714285714 Simplifying r = 0.5714285714Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Solution
r = {0.5714285714, 2.5}
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