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Simplifying 3r3 + 4r2 + 2r = 0 Reorder the terms: 2r + 4r2 + 3r3 = 0 Solving 2r + 4r2 + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(2 + 4r + 3r2) = 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 '(2 + 4r + 3r2)' equal to zero and attempt to solve: Simplifying 2 + 4r + 3r2 = 0 Solving 2 + 4r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 1.333333333r + r2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 1.333333333r + -0.6666666667 + r2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 1.333333333r + r2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 1.333333333r + r2 = 0 + -0.6666666667 1.333333333r + r2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 1.333333333r + r2 = -0.6666666667 The r term is 1.333333333r. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333r + 0.4444444442 + r2 = -0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333r + r2 = -0.6666666667 + 0.4444444442 Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225 0.4444444442 + 1.333333333r + r2 = -0.2222222225 Factor a perfect square on the left side: (r + 0.6666666665)(r + 0.6666666665) = -0.2222222225 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
r = {0}
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