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Simplifying -5t3 + 40t = 0 Reorder the terms: 40t + -5t3 = 0 Solving 40t + -5t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5t'. 5t(8 + -1t2) = 0 Ignore the factor 5.Subproblem 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 '(8 + -1t2)' equal to zero and attempt to solve: Simplifying 8 + -1t2 = 0 Solving 8 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t2 = 0 + -8 -1t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1t2 = -8 Divide each side by '-1'. t2 = 8 Simplifying t2 = 8 Take the square root of each side: t = {-2.828427125, 2.828427125}Solution
t = {0, -2.828427125, 2.828427125}
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