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Simplifying 0 = -16t2 + -29t + 170 Reorder the terms: 0 = 170 + -29t + -16t2 Solving 0 = 170 + -29t + -16t2 Solving for variable 't'. Combine like terms: 0 + -170 = -170 -170 + 29t + 16t2 = 170 + -29t + -16t2 + -170 + 29t + 16t2 Reorder the terms: -170 + 29t + 16t2 = 170 + -170 + -29t + 29t + -16t2 + 16t2 Combine like terms: 170 + -170 = 0 -170 + 29t + 16t2 = 0 + -29t + 29t + -16t2 + 16t2 -170 + 29t + 16t2 = -29t + 29t + -16t2 + 16t2 Combine like terms: -29t + 29t = 0 -170 + 29t + 16t2 = 0 + -16t2 + 16t2 -170 + 29t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -170 + 29t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.625 + 1.8125t + t2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + 1.8125t + 10.625 + t2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + 1.8125t + t2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + 1.8125t + t2 = 0 + 10.625 1.8125t + t2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 1.8125t + t2 = 10.625 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 = 10.625 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125t + t2 = 10.625 + 0.8212890625 Combine like terms: 10.625 + 0.8212890625 = 11.4462890625 0.8212890625 + 1.8125t + t2 = 11.4462890625 Factor a perfect square on the left side: (t + 0.90625)(t + 0.90625) = 11.4462890625 Calculate the square root of the right side: 3.383236477 Break this problem into two subproblems by setting (t + 0.90625) equal to 3.383236477 and -3.383236477.Subproblem 1
t + 0.90625 = 3.383236477 Simplifying t + 0.90625 = 3.383236477 Reorder the terms: 0.90625 + t = 3.383236477 Solving 0.90625 + t = 3.383236477 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 = 3.383236477 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + t = 3.383236477 + -0.90625 t = 3.383236477 + -0.90625 Combine like terms: 3.383236477 + -0.90625 = 2.476986477 t = 2.476986477 Simplifying t = 2.476986477Subproblem 2
t + 0.90625 = -3.383236477 Simplifying t + 0.90625 = -3.383236477 Reorder the terms: 0.90625 + t = -3.383236477 Solving 0.90625 + t = -3.383236477 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 = -3.383236477 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + t = -3.383236477 + -0.90625 t = -3.383236477 + -0.90625 Combine like terms: -3.383236477 + -0.90625 = -4.289486477 t = -4.289486477 Simplifying t = -4.289486477Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.476986477, -4.289486477}
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