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Simplifying 12t2 = 35t + 33 Reorder the terms: 12t2 = 33 + 35t Solving 12t2 = 33 + 35t Solving for variable 't'. Reorder the terms: -33 + -35t + 12t2 = 33 + 35t + -33 + -35t Reorder the terms: -33 + -35t + 12t2 = 33 + -33 + 35t + -35t Combine like terms: 33 + -33 = 0 -33 + -35t + 12t2 = 0 + 35t + -35t -33 + -35t + 12t2 = 35t + -35t Combine like terms: 35t + -35t = 0 -33 + -35t + 12t2 = 0 Factor a trinomial. (-3 + -4t)(11 + -3t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(11 + -3t)' equal to zero and attempt to solve: Simplifying 11 + -3t = 0 Solving 11 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -3t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -3t = 0 + -11 -3t = 0 + -11 Combine like terms: 0 + -11 = -11 -3t = -11 Divide each side by '-3'. t = 3.666666667 Simplifying t = 3.666666667Solution
t = {-0.75, 3.666666667}
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