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Simplifying -27r5 + 9r3 + -54r3 + -72r = 0 Reorder the terms: -72r + 9r3 + -54r3 + -27r5 = 0 Combine like terms: 9r3 + -54r3 = -45r3 -72r + -45r3 + -27r5 = 0 Solving -72r + -45r3 + -27r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '-9r'. -9r(8 + 5r2 + 3r4) = 0 Ignore the factor -9.Subproblem 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 '(8 + 5r2 + 3r4)' equal to zero and attempt to solve: Simplifying 8 + 5r2 + 3r4 = 0 Solving 8 + 5r2 + 3r4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 1.666666667r2 + r4 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 1.666666667r2 + -2.666666667 + r4 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 1.666666667r2 + r4 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 1.666666667r2 + r4 = 0 + -2.666666667 1.666666667r2 + r4 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 1.666666667r2 + r4 = -2.666666667 The r term is 1.666666667r2. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667r2 + 0.6944444447 + r4 = -2.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667r2 + r4 = -2.666666667 + 0.6944444447 Combine like terms: -2.666666667 + 0.6944444447 = -1.9722222223 0.6944444447 + 1.666666667r2 + r4 = -1.9722222223 Factor a perfect square on the left side: (r2 + 0.8333333335)(r2 + 0.8333333335) = -1.9722222223 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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