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Simplifying 96 = 32t + -2t2 Solving 96 = 32t + -2t2 Solving for variable 't'. Reorder the terms: 96 + -32t + 2t2 = 32t + -32t + -2t2 + 2t2 Combine like terms: 32t + -32t = 0 96 + -32t + 2t2 = 0 + -2t2 + 2t2 96 + -32t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 96 + -32t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -16t + t2) = 0 Factor a trinomial. 2((4 + -1t)(12 + -1t)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Solution
t = {4, 12}
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