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Simplifying 0 = -16t2 + -29t + 328 Reorder the terms: 0 = 328 + -29t + -16t2 Solving 0 = 328 + -29t + -16t2 Solving for variable 't'. Combine like terms: 0 + -328 = -328 -328 + 29t + 16t2 = 328 + -29t + -16t2 + -328 + 29t + 16t2 Reorder the terms: -328 + 29t + 16t2 = 328 + -328 + -29t + 29t + -16t2 + 16t2 Combine like terms: 328 + -328 = 0 -328 + 29t + 16t2 = 0 + -29t + 29t + -16t2 + 16t2 -328 + 29t + 16t2 = -29t + 29t + -16t2 + 16t2 Combine like terms: -29t + 29t = 0 -328 + 29t + 16t2 = 0 + -16t2 + 16t2 -328 + 29t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -328 + 29t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -20.5 + 1.8125t + t2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 1.8125t + 20.5 + t2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 1.8125t + t2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 1.8125t + t2 = 0 + 20.5 1.8125t + t2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 1.8125t + t2 = 20.5 The t term is 1.8125t. Take half its coefficient (0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. 1.8125t + 0.8212890625 + t2 = 20.5 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125t + t2 = 20.5 + 0.8212890625 Combine like terms: 20.5 + 0.8212890625 = 21.3212890625 0.8212890625 + 1.8125t + t2 = 21.3212890625 Factor a perfect square on the left side: (t + 0.90625)(t + 0.90625) = 21.3212890625 Calculate the square root of the right side: 4.617498139 Break this problem into two subproblems by setting (t + 0.90625) equal to 4.617498139 and -4.617498139.Subproblem 1
t + 0.90625 = 4.617498139 Simplifying t + 0.90625 = 4.617498139 Reorder the terms: 0.90625 + t = 4.617498139 Solving 0.90625 + t = 4.617498139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + t = 4.617498139 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + t = 4.617498139 + -0.90625 t = 4.617498139 + -0.90625 Combine like terms: 4.617498139 + -0.90625 = 3.711248139 t = 3.711248139 Simplifying t = 3.711248139Subproblem 2
t + 0.90625 = -4.617498139 Simplifying t + 0.90625 = -4.617498139 Reorder the terms: 0.90625 + t = -4.617498139 Solving 0.90625 + t = -4.617498139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + t = -4.617498139 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + t = -4.617498139 + -0.90625 t = -4.617498139 + -0.90625 Combine like terms: -4.617498139 + -0.90625 = -5.523748139 t = -5.523748139 Simplifying t = -5.523748139Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.711248139, -5.523748139}
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