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Simplifying (3r3 + -1r) + (4r + -5r3) = 0 Reorder the terms: (-1r + 3r3) + (4r + -5r3) = 0 Remove parenthesis around (-1r + 3r3) -1r + 3r3 + (4r + -5r3) = 0 Remove parenthesis around (4r + -5r3) -1r + 3r3 + 4r + -5r3 = 0 Reorder the terms: -1r + 4r + 3r3 + -5r3 = 0 Combine like terms: -1r + 4r = 3r 3r + 3r3 + -5r3 = 0 Combine like terms: 3r3 + -5r3 = -2r3 3r + -2r3 = 0 Solving 3r + -2r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(3 + -2r2) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(3 + -2r2)' equal to zero and attempt to solve: Simplifying 3 + -2r2 = 0 Solving 3 + -2r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r2 = 0 + -3 -2r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2r2 = -3 Divide each side by '-2'. r2 = 1.5 Simplifying r2 = 1.5 Take the square root of each side: r = {-1.224744871, 1.224744871}Solution
r = {0, -1.224744871, 1.224744871}
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