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Simplifying -16t2 + 368t + 12 = 1228 Reorder the terms: 12 + 368t + -16t2 = 1228 Solving 12 + 368t + -16t2 = 1228 Solving for variable 't'. Reorder the terms: 12 + -1228 + 368t + -16t2 = 1228 + -1228 Combine like terms: 12 + -1228 = -1216 -1216 + 368t + -16t2 = 1228 + -1228 Combine like terms: 1228 + -1228 = 0 -1216 + 368t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-76 + 23t + -1t2) = 0 Factor a trinomial. 16((-19 + t)(4 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-19 + t)' equal to zero and attempt to solve: Simplifying -19 + t = 0 Solving -19 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + t = 0 + 19 Combine like terms: -19 + 19 = 0 0 + t = 0 + 19 t = 0 + 19 Combine like terms: 0 + 19 = 19 t = 19 Simplifying t = 19Subproblem 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 = {19, 4}
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