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Simplifying 3r3 + -4r2 + 20r = 0 Reorder the terms: 20r + -4r2 + 3r3 = 0 Solving 20r + -4r2 + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(20 + -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 '(20 + -4r + 3r2)' equal to zero and attempt to solve: Simplifying 20 + -4r + 3r2 = 0 Solving 20 + -4r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6.666666667 + -1.333333333r + r2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + -1.333333333r + -6.666666667 + r2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + -1.333333333r + r2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + -1.333333333r + r2 = 0 + -6.666666667 -1.333333333r + r2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 -1.333333333r + r2 = -6.666666667 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 = -6.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333r + r2 = -6.666666667 + 0.4444444442 Combine like terms: -6.666666667 + 0.4444444442 = -6.2222222228 0.4444444442 + -1.333333333r + r2 = -6.2222222228 Factor a perfect square on the left side: (r + -0.6666666665)(r + -0.6666666665) = -6.2222222228 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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