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Simplifying 0 = 10r3 + -35r2 Reorder the terms: 0 = -35r2 + 10r3 Solving 0 = -35r2 + 10r3 Solving for variable 'r'. Remove the zero: 35r2 + -10r3 = -35r2 + 10r3 + 35r2 + -10r3 Reorder the terms: 35r2 + -10r3 = -35r2 + 35r2 + 10r3 + -10r3 Combine like terms: -35r2 + 35r2 = 0 35r2 + -10r3 = 0 + 10r3 + -10r3 35r2 + -10r3 = 10r3 + -10r3 Combine like terms: 10r3 + -10r3 = 0 35r2 + -10r3 = 0 Factor out the Greatest Common Factor (GCF), '5r2'. 5r2(7 + -2r) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}Subproblem 2
Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5Solution
r = {0, 3.5}
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