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Simplifying 45r2 + -69r = -20 + -4r2 + -6r Reorder the terms: -69r + 45r2 = -20 + -4r2 + -6r Reorder the terms: -69r + 45r2 = -20 + -6r + -4r2 Solving -69r + 45r2 = -20 + -6r + -4r2 Solving for variable 'r'. Reorder the terms: 20 + -69r + 6r + 45r2 + 4r2 = -20 + -6r + -4r2 + 20 + 6r + 4r2 Combine like terms: -69r + 6r = -63r 20 + -63r + 45r2 + 4r2 = -20 + -6r + -4r2 + 20 + 6r + 4r2 Combine like terms: 45r2 + 4r2 = 49r2 20 + -63r + 49r2 = -20 + -6r + -4r2 + 20 + 6r + 4r2 Reorder the terms: 20 + -63r + 49r2 = -20 + 20 + -6r + 6r + -4r2 + 4r2 Combine like terms: -20 + 20 = 0 20 + -63r + 49r2 = 0 + -6r + 6r + -4r2 + 4r2 20 + -63r + 49r2 = -6r + 6r + -4r2 + 4r2 Combine like terms: -6r + 6r = 0 20 + -63r + 49r2 = 0 + -4r2 + 4r2 20 + -63r + 49r2 = -4r2 + 4r2 Combine like terms: -4r2 + 4r2 = 0 20 + -63r + 49r2 = 0 Factor a trinomial. (4 + -7r)(5 + -7r) = 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 + -7r)' equal to zero and attempt to solve: Simplifying 5 + -7r = 0 Solving 5 + -7r = 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 + -7r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7r = 0 + -5 -7r = 0 + -5 Combine like terms: 0 + -5 = -5 -7r = -5 Divide each side by '-7'. r = 0.7142857143 Simplifying r = 0.7142857143Solution
r = {0.5714285714, 0.7142857143}
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