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Simplifying -16t2 + 55t + 34 = 0 Reorder the terms: 34 + 55t + -16t2 = 0 Solving 34 + 55t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.125 + -3.4375t + t2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -3.4375t + 2.125 + t2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -3.4375t + t2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -3.4375t + t2 = 0 + 2.125 -3.4375t + t2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -3.4375t + t2 = 2.125 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 = 2.125 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = 2.125 + 2.954101563 Combine like terms: 2.125 + 2.954101563 = 5.079101563 2.954101563 + -3.4375t + t2 = 5.079101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 5.079101563 Calculate the square root of the right side: 2.253686217 Break this problem into two subproblems by setting (t + -1.71875) equal to 2.253686217 and -2.253686217.Subproblem 1
t + -1.71875 = 2.253686217 Simplifying t + -1.71875 = 2.253686217 Reorder the terms: -1.71875 + t = 2.253686217 Solving -1.71875 + t = 2.253686217 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 = 2.253686217 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 2.253686217 + 1.71875 t = 2.253686217 + 1.71875 Combine like terms: 2.253686217 + 1.71875 = 3.972436217 t = 3.972436217 Simplifying t = 3.972436217Subproblem 2
t + -1.71875 = -2.253686217 Simplifying t + -1.71875 = -2.253686217 Reorder the terms: -1.71875 + t = -2.253686217 Solving -1.71875 + t = -2.253686217 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 = -2.253686217 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -2.253686217 + 1.71875 t = -2.253686217 + 1.71875 Combine like terms: -2.253686217 + 1.71875 = -0.534936217 t = -0.534936217 Simplifying t = -0.534936217Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.972436217, -0.534936217}
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