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Simplifying 1 = -16t2 + 33.3t Reorder the terms: 1 = 33.3t + -16t2 Solving 1 = 33.3t + -16t2 Solving for variable 't'. Reorder the terms: 1 + -33.3t + 16t2 = 33.3t + -33.3t + -16t2 + 16t2 Combine like terms: 33.3t + -33.3t = 0.0 1 + -33.3t + 16t2 = 0.0 + -16t2 + 16t2 1 + -33.3t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1 + -33.3t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -2.08125t + t2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -2.08125t + -0.0625 + t2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -2.08125t + t2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -2.08125t + t2 = 0 + -0.0625 -2.08125t + t2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -2.08125t + t2 = -0.0625 The t term is -2.08125t. Take half its coefficient (-1.040625). Square it (1.082900391) and add it to both sides. Add '1.082900391' to each side of the equation. -2.08125t + 1.082900391 + t2 = -0.0625 + 1.082900391 Reorder the terms: 1.082900391 + -2.08125t + t2 = -0.0625 + 1.082900391 Combine like terms: -0.0625 + 1.082900391 = 1.020400391 1.082900391 + -2.08125t + t2 = 1.020400391 Factor a perfect square on the left side: (t + -1.040625)(t + -1.040625) = 1.020400391 Calculate the square root of the right side: 1.010148697 Break this problem into two subproblems by setting (t + -1.040625) equal to 1.010148697 and -1.010148697.Subproblem 1
t + -1.040625 = 1.010148697 Simplifying t + -1.040625 = 1.010148697 Reorder the terms: -1.040625 + t = 1.010148697 Solving -1.040625 + t = 1.010148697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.040625' to each side of the equation. -1.040625 + 1.040625 + t = 1.010148697 + 1.040625 Combine like terms: -1.040625 + 1.040625 = 0.000000 0.000000 + t = 1.010148697 + 1.040625 t = 1.010148697 + 1.040625 Combine like terms: 1.010148697 + 1.040625 = 2.050773697 t = 2.050773697 Simplifying t = 2.050773697Subproblem 2
t + -1.040625 = -1.010148697 Simplifying t + -1.040625 = -1.010148697 Reorder the terms: -1.040625 + t = -1.010148697 Solving -1.040625 + t = -1.010148697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.040625' to each side of the equation. -1.040625 + 1.040625 + t = -1.010148697 + 1.040625 Combine like terms: -1.040625 + 1.040625 = 0.000000 0.000000 + t = -1.010148697 + 1.040625 t = -1.010148697 + 1.040625 Combine like terms: -1.010148697 + 1.040625 = 0.030476303 t = 0.030476303 Simplifying t = 0.030476303Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.050773697, 0.030476303}
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