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Simplifying 20t2 + 72t + -32 = 0 Reorder the terms: -32 + 72t + 20t2 = 0 Solving -32 + 72t + 20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 18t + 5t2) = 0 Factor a trinomial. 4((-4 + -1t)(2 + -5t)) = 0 Ignore the factor 4.Subproblem 1
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 = -4Subproblem 2
Set the factor '(2 + -5t)' equal to zero and attempt to solve: Simplifying 2 + -5t = 0 Solving 2 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5t = 0 + -2 -5t = 0 + -2 Combine like terms: 0 + -2 = -2 -5t = -2 Divide each side by '-5'. t = 0.4 Simplifying t = 0.4Solution
t = {-4, 0.4}
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