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Simplifying 20r4 + -41r2 + 20 = 0 Reorder the terms: 20 + -41r2 + 20r4 = 0 Solving 20 + -41r2 + 20r4 = 0 Solving for variable 'r'. Factor a trinomial. (4 + -5r2)(5 + -4r2) = 0Subproblem 1
Set the factor '(4 + -5r2)' equal to zero and attempt to solve: Simplifying 4 + -5r2 = 0 Solving 4 + -5r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5r2 = 0 + -4 -5r2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5r2 = -4 Divide each side by '-5'. r2 = 0.8 Simplifying r2 = 0.8 Take the square root of each side: r = {-0.894427191, 0.894427191}Subproblem 2
Set the factor '(5 + -4r2)' equal to zero and attempt to solve: Simplifying 5 + -4r2 = 0 Solving 5 + -4r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4r2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r2 = 0 + -5 -4r2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4r2 = -5 Divide each side by '-4'. r2 = 1.25 Simplifying r2 = 1.25 Take the square root of each side: r = {-1.118033989, 1.118033989}Solution
r = {-0.894427191, 0.894427191, -1.118033989, 1.118033989}
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