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Simplifying 10t2 = 32 + 32t Solving 10t2 = 32 + 32t Solving for variable 't'. Reorder the terms: -32 + -32t + 10t2 = 32 + 32t + -32 + -32t Reorder the terms: -32 + -32t + 10t2 = 32 + -32 + 32t + -32t Combine like terms: 32 + -32 = 0 -32 + -32t + 10t2 = 0 + 32t + -32t -32 + -32t + 10t2 = 32t + -32t Combine like terms: 32t + -32t = 0 -32 + -32t + 10t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -16t + 5t2) = 0 Factor a trinomial. 2((-4 + -5t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5t)' equal to zero and attempt to solve: Simplifying -4 + -5t = 0 Solving -4 + -5t = 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 + -5t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5t = 0 + 4 -5t = 0 + 4 Combine like terms: 0 + 4 = 4 -5t = 4 Divide each side by '-5'. t = -0.8 Simplifying t = -0.8Subproblem 2
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 = {-0.8, 4}
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