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Simplifying 52 = -16t2 + 56t + 3 Reorder the terms: 52 = 3 + 56t + -16t2 Solving 52 = 3 + 56t + -16t2 Solving for variable 't'. Combine like terms: 52 + -3 = 49 49 + -56t + 16t2 = 3 + 56t + -16t2 + -3 + -56t + 16t2 Reorder the terms: 49 + -56t + 16t2 = 3 + -3 + 56t + -56t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 49 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2 49 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 49 + -56t + 16t2 = 0 + -16t2 + 16t2 49 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 49 + -56t + 16t2 = 0 Factor a trinomial. (7 + -4t)(7 + -4t) = 0Subproblem 1
Set the factor '(7 + -4t)' equal to zero and attempt to solve: Simplifying 7 + -4t = 0 Solving 7 + -4t = 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 + -4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t = 0 + -7 -4t = 0 + -7 Combine like terms: 0 + -7 = -7 -4t = -7 Divide each side by '-4'. t = 1.75 Simplifying t = 1.75Subproblem 2
Set the factor '(7 + -4t)' equal to zero and attempt to solve: Simplifying 7 + -4t = 0 Solving 7 + -4t = 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 + -4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t = 0 + -7 -4t = 0 + -7 Combine like terms: 0 + -7 = -7 -4t = -7 Divide each side by '-4'. t = 1.75 Simplifying t = 1.75Solution
t = {1.75, 1.75}
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