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Simplifying 20r4 + -39r2 + 18r2 = 0 Reorder the terms: -39r2 + 18r2 + 20r4 = 0 Combine like terms: -39r2 + 18r2 = -21r2 -21r2 + 20r4 = 0 Solving -21r2 + 20r4 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r2'. r2(-21 + 20r2) = 0Subproblem 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 '(-21 + 20r2)' equal to zero and attempt to solve: Simplifying -21 + 20r2 = 0 Solving -21 + 20r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 20r2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 20r2 = 0 + 21 20r2 = 0 + 21 Combine like terms: 0 + 21 = 21 20r2 = 21 Divide each side by '20'. r2 = 1.05 Simplifying r2 = 1.05 Take the square root of each side: r = {-1.024695077, 1.024695077}Solution
r = {0, -1.024695077, 1.024695077}
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