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Simplifying 0 = 4928 + -1152t + 64t2 Solving 0 = 4928 + -1152t + 64t2 Solving for variable 't'. Combine like terms: 0 + -4928 = -4928 -4928 + 1152t + -64t2 = 4928 + -1152t + 64t2 + -4928 + 1152t + -64t2 Reorder the terms: -4928 + 1152t + -64t2 = 4928 + -4928 + -1152t + 1152t + 64t2 + -64t2 Combine like terms: 4928 + -4928 = 0 -4928 + 1152t + -64t2 = 0 + -1152t + 1152t + 64t2 + -64t2 -4928 + 1152t + -64t2 = -1152t + 1152t + 64t2 + -64t2 Combine like terms: -1152t + 1152t = 0 -4928 + 1152t + -64t2 = 0 + 64t2 + -64t2 -4928 + 1152t + -64t2 = 64t2 + -64t2 Combine like terms: 64t2 + -64t2 = 0 -4928 + 1152t + -64t2 = 0 Factor out the Greatest Common Factor (GCF), '64'. 64(-77 + 18t + -1t2) = 0 Factor a trinomial. 64((-11 + t)(7 + -1t)) = 0 Ignore the factor 64.Subproblem 1
Set the factor '(-11 + t)' equal to zero and attempt to solve: Simplifying -11 + t = 0 Solving -11 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + t = 0 + 11 t = 0 + 11 Combine like terms: 0 + 11 = 11 t = 11 Simplifying t = 11Subproblem 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 = {11, 7}
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