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Simplifying 0 = -16t2 + 55t + -26 Reorder the terms: 0 = -26 + 55t + -16t2 Solving 0 = -26 + 55t + -16t2 Solving for variable 't'. Combine like terms: 0 + 26 = 26 26 + -55t + 16t2 = -26 + 55t + -16t2 + 26 + -55t + 16t2 Reorder the terms: 26 + -55t + 16t2 = -26 + 26 + 55t + -55t + -16t2 + 16t2 Combine like terms: -26 + 26 = 0 26 + -55t + 16t2 = 0 + 55t + -55t + -16t2 + 16t2 26 + -55t + 16t2 = 55t + -55t + -16t2 + 16t2 Combine like terms: 55t + -55t = 0 26 + -55t + 16t2 = 0 + -16t2 + 16t2 26 + -55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 26 + -55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.625 + -3.4375t + t2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -3.4375t + -1.625 + t2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -3.4375t + t2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -3.4375t + t2 = 0 + -1.625 -3.4375t + t2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -3.4375t + t2 = -1.625 The t term is -3.4375t. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375t + 2.954101563 + t2 = -1.625 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = -1.625 + 2.954101563 Combine like terms: -1.625 + 2.954101563 = 1.329101563 2.954101563 + -3.4375t + t2 = 1.329101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 1.329101563 Calculate the square root of the right side: 1.152866672 Break this problem into two subproblems by setting (t + -1.71875) equal to 1.152866672 and -1.152866672.Subproblem 1
t + -1.71875 = 1.152866672 Simplifying t + -1.71875 = 1.152866672 Reorder the terms: -1.71875 + t = 1.152866672 Solving -1.71875 + t = 1.152866672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = 1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 1.152866672 + 1.71875 t = 1.152866672 + 1.71875 Combine like terms: 1.152866672 + 1.71875 = 2.871616672 t = 2.871616672 Simplifying t = 2.871616672Subproblem 2
t + -1.71875 = -1.152866672 Simplifying t + -1.71875 = -1.152866672 Reorder the terms: -1.71875 + t = -1.152866672 Solving -1.71875 + t = -1.152866672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = -1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -1.152866672 + 1.71875 t = -1.152866672 + 1.71875 Combine like terms: -1.152866672 + 1.71875 = 0.565883328 t = 0.565883328 Simplifying t = 0.565883328Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.871616672, 0.565883328}
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