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Simplifying (2t + -3)(2t + -3) = 2t2 + 5t + -26 Reorder the terms: (-3 + 2t)(2t + -3) = 2t2 + 5t + -26 Reorder the terms: (-3 + 2t)(-3 + 2t) = 2t2 + 5t + -26 Multiply (-3 + 2t) * (-3 + 2t) (-3(-3 + 2t) + 2t * (-3 + 2t)) = 2t2 + 5t + -26 ((-3 * -3 + 2t * -3) + 2t * (-3 + 2t)) = 2t2 + 5t + -26 ((9 + -6t) + 2t * (-3 + 2t)) = 2t2 + 5t + -26 (9 + -6t + (-3 * 2t + 2t * 2t)) = 2t2 + 5t + -26 (9 + -6t + (-6t + 4t2)) = 2t2 + 5t + -26 Combine like terms: -6t + -6t = -12t (9 + -12t + 4t2) = 2t2 + 5t + -26 Reorder the terms: 9 + -12t + 4t2 = -26 + 5t + 2t2 Solving 9 + -12t + 4t2 = -26 + 5t + 2t2 Solving for variable 't'. Reorder the terms: 9 + 26 + -12t + -5t + 4t2 + -2t2 = -26 + 5t + 2t2 + 26 + -5t + -2t2 Combine like terms: 9 + 26 = 35 35 + -12t + -5t + 4t2 + -2t2 = -26 + 5t + 2t2 + 26 + -5t + -2t2 Combine like terms: -12t + -5t = -17t 35 + -17t + 4t2 + -2t2 = -26 + 5t + 2t2 + 26 + -5t + -2t2 Combine like terms: 4t2 + -2t2 = 2t2 35 + -17t + 2t2 = -26 + 5t + 2t2 + 26 + -5t + -2t2 Reorder the terms: 35 + -17t + 2t2 = -26 + 26 + 5t + -5t + 2t2 + -2t2 Combine like terms: -26 + 26 = 0 35 + -17t + 2t2 = 0 + 5t + -5t + 2t2 + -2t2 35 + -17t + 2t2 = 5t + -5t + 2t2 + -2t2 Combine like terms: 5t + -5t = 0 35 + -17t + 2t2 = 0 + 2t2 + -2t2 35 + -17t + 2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 35 + -17t + 2t2 = 0 Factor a trinomial. (7 + -2t)(5 + -1t) = 0Subproblem 1
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 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 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {3.5, 5}
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