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Simplifying -16t2 + 70t + 3 = 50 Reorder the terms: 3 + 70t + -16t2 = 50 Solving 3 + 70t + -16t2 = 50 Solving for variable 't'. Reorder the terms: 3 + -50 + 70t + -16t2 = 50 + -50 Combine like terms: 3 + -50 = -47 -47 + 70t + -16t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -47 + 70t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.9375 + -4.375t + t2 = 0 Move the constant term to the right: Add '-2.9375' to each side of the equation. 2.9375 + -4.375t + -2.9375 + t2 = 0 + -2.9375 Reorder the terms: 2.9375 + -2.9375 + -4.375t + t2 = 0 + -2.9375 Combine like terms: 2.9375 + -2.9375 = 0.0000 0.0000 + -4.375t + t2 = 0 + -2.9375 -4.375t + t2 = 0 + -2.9375 Combine like terms: 0 + -2.9375 = -2.9375 -4.375t + t2 = -2.9375 The t term is -4.375t. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375t + 4.78515625 + t2 = -2.9375 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = -2.9375 + 4.78515625 Combine like terms: -2.9375 + 4.78515625 = 1.84765625 4.78515625 + -4.375t + t2 = 1.84765625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 1.84765625 Calculate the square root of the right side: 1.359285198 Break this problem into two subproblems by setting (t + -2.1875) equal to 1.359285198 and -1.359285198.Subproblem 1
t + -2.1875 = 1.359285198 Simplifying t + -2.1875 = 1.359285198 Reorder the terms: -2.1875 + t = 1.359285198 Solving -2.1875 + t = 1.359285198 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = 1.359285198 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 1.359285198 + 2.1875 t = 1.359285198 + 2.1875 Combine like terms: 1.359285198 + 2.1875 = 3.546785198 t = 3.546785198 Simplifying t = 3.546785198Subproblem 2
t + -2.1875 = -1.359285198 Simplifying t + -2.1875 = -1.359285198 Reorder the terms: -2.1875 + t = -1.359285198 Solving -2.1875 + t = -1.359285198 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = -1.359285198 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -1.359285198 + 2.1875 t = -1.359285198 + 2.1875 Combine like terms: -1.359285198 + 2.1875 = 0.828214802 t = 0.828214802 Simplifying t = 0.828214802Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.546785198, 0.828214802}
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