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Simplifying 37r2 + -33r + -7 = 1 + 2r2 Reorder the terms: -7 + -33r + 37r2 = 1 + 2r2 Solving -7 + -33r + 37r2 = 1 + 2r2 Solving for variable 'r'. Reorder the terms: -7 + -1 + -33r + 37r2 + -2r2 = 1 + 2r2 + -1 + -2r2 Combine like terms: -7 + -1 = -8 -8 + -33r + 37r2 + -2r2 = 1 + 2r2 + -1 + -2r2 Combine like terms: 37r2 + -2r2 = 35r2 -8 + -33r + 35r2 = 1 + 2r2 + -1 + -2r2 Reorder the terms: -8 + -33r + 35r2 = 1 + -1 + 2r2 + -2r2 Combine like terms: 1 + -1 = 0 -8 + -33r + 35r2 = 0 + 2r2 + -2r2 -8 + -33r + 35r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -8 + -33r + 35r2 = 0 Factor a trinomial. (-1 + -5r)(8 + -7r) = 0Subproblem 1
Set the factor '(-1 + -5r)' equal to zero and attempt to solve: Simplifying -1 + -5r = 0 Solving -1 + -5r = 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 + -5r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5r = 0 + 1 -5r = 0 + 1 Combine like terms: 0 + 1 = 1 -5r = 1 Divide each side by '-5'. r = -0.2 Simplifying r = -0.2Subproblem 2
Set the factor '(8 + -7r)' equal to zero and attempt to solve: Simplifying 8 + -7r = 0 Solving 8 + -7r = 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 + -7r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7r = 0 + -8 -7r = 0 + -8 Combine like terms: 0 + -8 = -8 -7r = -8 Divide each side by '-7'. r = 1.142857143 Simplifying r = 1.142857143Solution
r = {-0.2, 1.142857143}
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