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Simplifying 0 = -16t2 + 16t + 672 Reorder the terms: 0 = 672 + 16t + -16t2 Solving 0 = 672 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -672 = -672 -672 + -16t + 16t2 = 672 + 16t + -16t2 + -672 + -16t + 16t2 Reorder the terms: -672 + -16t + 16t2 = 672 + -672 + 16t + -16t + -16t2 + 16t2 Combine like terms: 672 + -672 = 0 -672 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -672 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -672 + -16t + 16t2 = 0 + -16t2 + 16t2 -672 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -672 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-42 + -1t + t2) = 0 Factor a trinomial. 16((-6 + -1t)(7 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve: Simplifying -6 + -1t = 0 Solving -6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1t = 0 + 6 -1t = 0 + 6 Combine like terms: 0 + 6 = 6 -1t = 6 Divide each side by '-1'. t = -6 Simplifying t = -6Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-6, 7}
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