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Simplifying 294 = -16t2 + 34t + 336 Reorder the terms: 294 = 336 + 34t + -16t2 Solving 294 = 336 + 34t + -16t2 Solving for variable 't'. Combine like terms: 294 + -336 = -42 -42 + -34t + 16t2 = 336 + 34t + -16t2 + -336 + -34t + 16t2 Reorder the terms: -42 + -34t + 16t2 = 336 + -336 + 34t + -34t + -16t2 + 16t2 Combine like terms: 336 + -336 = 0 -42 + -34t + 16t2 = 0 + 34t + -34t + -16t2 + 16t2 -42 + -34t + 16t2 = 34t + -34t + -16t2 + 16t2 Combine like terms: 34t + -34t = 0 -42 + -34t + 16t2 = 0 + -16t2 + 16t2 -42 + -34t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -42 + -34t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -17t + 8t2) = 0 Factor a trinomial. 2((-7 + -8t)(3 + -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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.875, 3}
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