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Simplifying t5 + 80t + -21t3 = 0 Reorder the terms: 80t + -21t3 + t5 = 0 Solving 80t + -21t3 + t5 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(80 + -21t2 + t4) = 0 Factor a trinomial. t((5 + -1t2)(16 + -1t2)) = 0 Factor a difference between two squares. t((5 + -1t2)((4 + t)(4 + -1t))) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(5 + -1t2)' equal to zero and attempt to solve: Simplifying 5 + -1t2 = 0 Solving 5 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t2 = 0 + -5 -1t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1t2 = -5 Divide each side by '-1'. t2 = 5 Simplifying t2 = 5 Take the square root of each side: t = {-2.236067978, 2.236067978}Subproblem 3
Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4Subproblem 4
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {0, -2.236067978, 2.236067978, -4, 4}
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