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Simplifying 200 = -16t2 + 117t + 2 Reorder the terms: 200 = 2 + 117t + -16t2 Solving 200 = 2 + 117t + -16t2 Solving for variable 't'. Combine like terms: 200 + -2 = 198 198 + -117t + 16t2 = 2 + 117t + -16t2 + -2 + -117t + 16t2 Reorder the terms: 198 + -117t + 16t2 = 2 + -2 + 117t + -117t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 198 + -117t + 16t2 = 0 + 117t + -117t + -16t2 + 16t2 198 + -117t + 16t2 = 117t + -117t + -16t2 + 16t2 Combine like terms: 117t + -117t = 0 198 + -117t + 16t2 = 0 + -16t2 + 16t2 198 + -117t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 198 + -117t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 12.375 + -7.3125t + t2 = 0 Move the constant term to the right: Add '-12.375' to each side of the equation. 12.375 + -7.3125t + -12.375 + t2 = 0 + -12.375 Reorder the terms: 12.375 + -12.375 + -7.3125t + t2 = 0 + -12.375 Combine like terms: 12.375 + -12.375 = 0.000 0.000 + -7.3125t + t2 = 0 + -12.375 -7.3125t + t2 = 0 + -12.375 Combine like terms: 0 + -12.375 = -12.375 -7.3125t + t2 = -12.375 The t term is -7.3125t. Take half its coefficient (-3.65625). Square it (13.36816406) and add it to both sides. Add '13.36816406' to each side of the equation. -7.3125t + 13.36816406 + t2 = -12.375 + 13.36816406 Reorder the terms: 13.36816406 + -7.3125t + t2 = -12.375 + 13.36816406 Combine like terms: -12.375 + 13.36816406 = 0.99316406 13.36816406 + -7.3125t + t2 = 0.99316406 Factor a perfect square on the left side: (t + -3.65625)(t + -3.65625) = 0.99316406 Calculate the square root of the right side: 0.996576169 Break this problem into two subproblems by setting (t + -3.65625) equal to 0.996576169 and -0.996576169.Subproblem 1
t + -3.65625 = 0.996576169 Simplifying t + -3.65625 = 0.996576169 Reorder the terms: -3.65625 + t = 0.996576169 Solving -3.65625 + t = 0.996576169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = 0.996576169 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = 0.996576169 + 3.65625 t = 0.996576169 + 3.65625 Combine like terms: 0.996576169 + 3.65625 = 4.652826169 t = 4.652826169 Simplifying t = 4.652826169Subproblem 2
t + -3.65625 = -0.996576169 Simplifying t + -3.65625 = -0.996576169 Reorder the terms: -3.65625 + t = -0.996576169 Solving -3.65625 + t = -0.996576169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = -0.996576169 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = -0.996576169 + 3.65625 t = -0.996576169 + 3.65625 Combine like terms: -0.996576169 + 3.65625 = 2.659673831 t = 2.659673831 Simplifying t = 2.659673831Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.652826169, 2.659673831}
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