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Simplifying 40t2 + -24t + -64 = 0 Reorder the terms: -64 + -24t + 40t2 = 0 Solving -64 + -24t + 40t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-8 + -3t + 5t2) = 0 Factor a trinomial. 8((-1 + -1t)(8 + -5t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
Set the factor '(8 + -5t)' equal to zero and attempt to solve: Simplifying 8 + -5t = 0 Solving 8 + -5t = 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 + -5t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5t = 0 + -8 -5t = 0 + -8 Combine like terms: 0 + -8 = -8 -5t = -8 Divide each side by '-5'. t = 1.6 Simplifying t = 1.6Solution
t = {-1, 1.6}
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