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Simplifying 200 = 16t2 + -4.5t + 74 Reorder the terms: 200 = 74 + -4.5t + 16t2 Solving 200 = 74 + -4.5t + 16t2 Solving for variable 't'. Combine like terms: 200 + -74 = 126 126 + 4.5t + -16t2 = 74 + -4.5t + 16t2 + -74 + 4.5t + -16t2 Reorder the terms: 126 + 4.5t + -16t2 = 74 + -74 + -4.5t + 4.5t + 16t2 + -16t2 Combine like terms: 74 + -74 = 0 126 + 4.5t + -16t2 = 0 + -4.5t + 4.5t + 16t2 + -16t2 126 + 4.5t + -16t2 = -4.5t + 4.5t + 16t2 + -16t2 Combine like terms: -4.5t + 4.5t = 0.0 126 + 4.5t + -16t2 = 0.0 + 16t2 + -16t2 126 + 4.5t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 126 + 4.5t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7.875 + -0.28125t + t2 = 0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + -0.28125t + 7.875 + t2 = 0 + 7.875 Reorder the terms: -7.875 + 7.875 + -0.28125t + t2 = 0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + -0.28125t + t2 = 0 + 7.875 -0.28125t + t2 = 0 + 7.875 Combine like terms: 0 + 7.875 = 7.875 -0.28125t + t2 = 7.875 The t term is -0.28125t. Take half its coefficient (-0.140625). Square it (0.01977539063) and add it to both sides. Add '0.01977539063' to each side of the equation. -0.28125t + 0.01977539063 + t2 = 7.875 + 0.01977539063 Reorder the terms: 0.01977539063 + -0.28125t + t2 = 7.875 + 0.01977539063 Combine like terms: 7.875 + 0.01977539063 = 7.89477539063 0.01977539063 + -0.28125t + t2 = 7.89477539063 Factor a perfect square on the left side: (t + -0.140625)(t + -0.140625) = 7.89477539063 Calculate the square root of the right side: 2.809764294 Break this problem into two subproblems by setting (t + -0.140625) equal to 2.809764294 and -2.809764294.Subproblem 1
t + -0.140625 = 2.809764294 Simplifying t + -0.140625 = 2.809764294 Reorder the terms: -0.140625 + t = 2.809764294 Solving -0.140625 + t = 2.809764294 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.140625' to each side of the equation. -0.140625 + 0.140625 + t = 2.809764294 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + t = 2.809764294 + 0.140625 t = 2.809764294 + 0.140625 Combine like terms: 2.809764294 + 0.140625 = 2.950389294 t = 2.950389294 Simplifying t = 2.950389294Subproblem 2
t + -0.140625 = -2.809764294 Simplifying t + -0.140625 = -2.809764294 Reorder the terms: -0.140625 + t = -2.809764294 Solving -0.140625 + t = -2.809764294 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.140625' to each side of the equation. -0.140625 + 0.140625 + t = -2.809764294 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + t = -2.809764294 + 0.140625 t = -2.809764294 + 0.140625 Combine like terms: -2.809764294 + 0.140625 = -2.669139294 t = -2.669139294 Simplifying t = -2.669139294Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.950389294, -2.669139294}
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