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Simplifying 44 = -16t2 + 148t + 17 Reorder the terms: 44 = 17 + 148t + -16t2 Solving 44 = 17 + 148t + -16t2 Solving for variable 't'. Combine like terms: 44 + -17 = 27 27 + -148t + 16t2 = 17 + 148t + -16t2 + -17 + -148t + 16t2 Reorder the terms: 27 + -148t + 16t2 = 17 + -17 + 148t + -148t + -16t2 + 16t2 Combine like terms: 17 + -17 = 0 27 + -148t + 16t2 = 0 + 148t + -148t + -16t2 + 16t2 27 + -148t + 16t2 = 148t + -148t + -16t2 + 16t2 Combine like terms: 148t + -148t = 0 27 + -148t + 16t2 = 0 + -16t2 + 16t2 27 + -148t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 27 + -148t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.6875 + -9.25t + t2 = 0 Move the constant term to the right: Add '-1.6875' to each side of the equation. 1.6875 + -9.25t + -1.6875 + t2 = 0 + -1.6875 Reorder the terms: 1.6875 + -1.6875 + -9.25t + t2 = 0 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + -9.25t + t2 = 0 + -1.6875 -9.25t + t2 = 0 + -1.6875 Combine like terms: 0 + -1.6875 = -1.6875 -9.25t + t2 = -1.6875 The t term is -9.25t. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25t + 21.390625 + t2 = -1.6875 + 21.390625 Reorder the terms: 21.390625 + -9.25t + t2 = -1.6875 + 21.390625 Combine like terms: -1.6875 + 21.390625 = 19.703125 21.390625 + -9.25t + t2 = 19.703125 Factor a perfect square on the left side: (t + -4.625)(t + -4.625) = 19.703125 Calculate the square root of the right side: 4.438820226 Break this problem into two subproblems by setting (t + -4.625) equal to 4.438820226 and -4.438820226.Subproblem 1
t + -4.625 = 4.438820226 Simplifying t + -4.625 = 4.438820226 Reorder the terms: -4.625 + t = 4.438820226 Solving -4.625 + t = 4.438820226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = 4.438820226 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = 4.438820226 + 4.625 t = 4.438820226 + 4.625 Combine like terms: 4.438820226 + 4.625 = 9.063820226 t = 9.063820226 Simplifying t = 9.063820226Subproblem 2
t + -4.625 = -4.438820226 Simplifying t + -4.625 = -4.438820226 Reorder the terms: -4.625 + t = -4.438820226 Solving -4.625 + t = -4.438820226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = -4.438820226 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = -4.438820226 + 4.625 t = -4.438820226 + 4.625 Combine like terms: -4.438820226 + 4.625 = 0.186179774 t = 0.186179774 Simplifying t = 0.186179774Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.063820226, 0.186179774}
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