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Simplifying -16t2 + 176t = 448 Reorder the terms: 176t + -16t2 = 448 Solving 176t + -16t2 = 448 Solving for variable 't'. Reorder the terms: -448 + 176t + -16t2 = 448 + -448 Combine like terms: 448 + -448 = 0 -448 + 176t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-28 + 11t + -1t2) = 0 Factor a trinomial. 16((-7 + t)(4 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 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 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Subproblem 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 = {7, 4}
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