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Simplifying 16t2 + -248t + 232 = 0 Reorder the terms: 232 + -248t + 16t2 = 0 Solving 232 + -248t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(29 + -31t + 2t2) = 0 Factor a trinomial. 8((1 + -1t)(29 + -2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(29 + -2t)' equal to zero and attempt to solve: Simplifying 29 + -2t = 0 Solving 29 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -2t = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -2t = 0 + -29 -2t = 0 + -29 Combine like terms: 0 + -29 = -29 -2t = -29 Divide each side by '-2'. t = 14.5 Simplifying t = 14.5Solution
t = {1, 14.5}
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