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Simplifying -16t2 + 55t + 2 = 0 Reorder the terms: 2 + 55t + -16t2 = 0 Solving 2 + 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'. -0.125 + -3.4375t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.4375t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.4375t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.4375t + t2 = 0 + 0.125 -3.4375t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.4375t + t2 = 0.125 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 = 0.125 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = 0.125 + 2.954101563 Combine like terms: 0.125 + 2.954101563 = 3.079101563 2.954101563 + -3.4375t + t2 = 3.079101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 3.079101563 Calculate the square root of the right side: 1.754736893 Break this problem into two subproblems by setting (t + -1.71875) equal to 1.754736893 and -1.754736893.Subproblem 1
t + -1.71875 = 1.754736893 Simplifying t + -1.71875 = 1.754736893 Reorder the terms: -1.71875 + t = 1.754736893 Solving -1.71875 + t = 1.754736893 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 = 1.754736893 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 1.754736893 + 1.71875 t = 1.754736893 + 1.71875 Combine like terms: 1.754736893 + 1.71875 = 3.473486893 t = 3.473486893 Simplifying t = 3.473486893Subproblem 2
t + -1.71875 = -1.754736893 Simplifying t + -1.71875 = -1.754736893 Reorder the terms: -1.71875 + t = -1.754736893 Solving -1.71875 + t = -1.754736893 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 = -1.754736893 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -1.754736893 + 1.71875 t = -1.754736893 + 1.71875 Combine like terms: -1.754736893 + 1.71875 = -0.035986893 t = -0.035986893 Simplifying t = -0.035986893Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.473486893, -0.035986893}
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