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Simplifying 5x3 + 70x2r + 245xr2 = 0 Reorder the terms: 70rx2 + 245r2x + 5x3 = 0 Solving 70rx2 + 245r2x + 5x3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(14rx + 49r2 + x2) = 0 Factor a trinomial. 5x((7r + x)(7r + x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing r to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7r + x)' equal to zero and attempt to solve: Simplifying 7r + x = 0 Solving 7r + x = 0 Move all terms containing r to the left, all other terms to the right. Add '-1x' to each side of the equation. 7r + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 7r + 0 = 0 + -1x 7r = 0 + -1x Remove the zero: 7r = -1x Divide each side by '7'. r = -0.1428571429x Simplifying r = -0.1428571429xSubproblem 3
Set the factor '(7r + x)' equal to zero and attempt to solve: Simplifying 7r + x = 0 Solving 7r + x = 0 Move all terms containing r to the left, all other terms to the right. Add '-1x' to each side of the equation. 7r + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 7r + 0 = 0 + -1x 7r = 0 + -1x Remove the zero: 7r = -1x Divide each side by '7'. r = -0.1428571429x Simplifying r = -0.1428571429xSolution
r = {-0.1428571429x, -0.1428571429x}
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