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Simplifying 16t2 + -46t + 28 = 0 Reorder the terms: 28 + -46t + 16t2 = 0 Solving 28 + -46t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -23t + 8t2) = 0 Factor a trinomial. 2((7 + -8t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -8t)' equal to zero and attempt to solve: Simplifying 7 + -8t = 0 Solving 7 + -8t = 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 + -8t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8t = 0 + -7 -8t = 0 + -7 Combine like terms: 0 + -7 = -7 -8t = -7 Divide each side by '-8'. t = 0.875 Simplifying t = 0.875Subproblem 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 = {0.875, 2}
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