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Simplifying 112 = -16t2 + 64t + 48 Reorder the terms: 112 = 48 + 64t + -16t2 Solving 112 = 48 + 64t + -16t2 Solving for variable 't'. Combine like terms: 112 + -48 = 64 64 + -64t + 16t2 = 48 + 64t + -16t2 + -48 + -64t + 16t2 Reorder the terms: 64 + -64t + 16t2 = 48 + -48 + 64t + -64t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 64 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 64 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 64 + -64t + 16t2 = 0 + -16t2 + 16t2 64 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 64 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(4 + -4t + t2) = 0 Factor a trinomial. 16((2 + -1t)(2 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {2, 2}
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