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Simplifying 20s4 + -41s2 + 20 = 0 Reorder the terms: 20 + -41s2 + 20s4 = 0 Solving 20 + -41s2 + 20s4 = 0 Solving for variable 's'. Factor a trinomial. (4 + -5s2)(5 + -4s2) = 0Subproblem 1
Set the factor '(4 + -5s2)' equal to zero and attempt to solve: Simplifying 4 + -5s2 = 0 Solving 4 + -5s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5s2 = 0 + -4 -5s2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5s2 = -4 Divide each side by '-5'. s2 = 0.8 Simplifying s2 = 0.8 Take the square root of each side: s = {-0.894427191, 0.894427191}Subproblem 2
Set the factor '(5 + -4s2)' equal to zero and attempt to solve: Simplifying 5 + -4s2 = 0 Solving 5 + -4s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4s2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4s2 = 0 + -5 -4s2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4s2 = -5 Divide each side by '-4'. s2 = 1.25 Simplifying s2 = 1.25 Take the square root of each side: s = {-1.118033989, 1.118033989}Solution
s = {-0.894427191, 0.894427191, -1.118033989, 1.118033989}
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