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Simplifying 0 = -16t2 + 55t + 6 Reorder the terms: 0 = 6 + 55t + -16t2 Solving 0 = 6 + 55t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -55t + 16t2 = 6 + 55t + -16t2 + -6 + -55t + 16t2 Reorder the terms: -6 + -55t + 16t2 = 6 + -6 + 55t + -55t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -55t + 16t2 = 0 + 55t + -55t + -16t2 + 16t2 -6 + -55t + 16t2 = 55t + -55t + -16t2 + 16t2 Combine like terms: 55t + -55t = 0 -6 + -55t + 16t2 = 0 + -16t2 + 16t2 -6 + -55t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -55t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -3.4375t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.4375t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.4375t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.4375t + t2 = 0 + 0.375 -3.4375t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.4375t + t2 = 0.375 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 = 0.375 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = 0.375 + 2.954101563 Combine like terms: 0.375 + 2.954101563 = 3.329101563 2.954101563 + -3.4375t + t2 = 3.329101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 3.329101563 Calculate the square root of the right side: 1.824582572 Break this problem into two subproblems by setting (t + -1.71875) equal to 1.824582572 and -1.824582572.Subproblem 1
t + -1.71875 = 1.824582572 Simplifying t + -1.71875 = 1.824582572 Reorder the terms: -1.71875 + t = 1.824582572 Solving -1.71875 + t = 1.824582572 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 = 1.824582572 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 1.824582572 + 1.71875 t = 1.824582572 + 1.71875 Combine like terms: 1.824582572 + 1.71875 = 3.543332572 t = 3.543332572 Simplifying t = 3.543332572Subproblem 2
t + -1.71875 = -1.824582572 Simplifying t + -1.71875 = -1.824582572 Reorder the terms: -1.71875 + t = -1.824582572 Solving -1.71875 + t = -1.824582572 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 = -1.824582572 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -1.824582572 + 1.71875 t = -1.824582572 + 1.71875 Combine like terms: -1.824582572 + 1.71875 = -0.105832572 t = -0.105832572 Simplifying t = -0.105832572Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.543332572, -0.105832572}
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