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Simplifying 432 = -16t2 + 28t + 576 Reorder the terms: 432 = 576 + 28t + -16t2 Solving 432 = 576 + 28t + -16t2 Solving for variable 't'. Combine like terms: 432 + -576 = -144 -144 + -28t + 16t2 = 576 + 28t + -16t2 + -576 + -28t + 16t2 Reorder the terms: -144 + -28t + 16t2 = 576 + -576 + 28t + -28t + -16t2 + 16t2 Combine like terms: 576 + -576 = 0 -144 + -28t + 16t2 = 0 + 28t + -28t + -16t2 + 16t2 -144 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2 Combine like terms: 28t + -28t = 0 -144 + -28t + 16t2 = 0 + -16t2 + 16t2 -144 + -28t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144 + -28t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + -7t + 4t2) = 0 Factor a trinomial. 4((-9 + -4t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve: Simplifying -9 + -4t = 0 Solving -9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t = 0 + 9 -4t = 0 + 9 Combine like terms: 0 + 9 = 9 -4t = 9 Divide each side by '-4'. t = -2.25 Simplifying t = -2.25Subproblem 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 = {-2.25, 4}
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