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Simplifying 0 = -16t2 + -11t + 190 Reorder the terms: 0 = 190 + -11t + -16t2 Solving 0 = 190 + -11t + -16t2 Solving for variable 't'. Combine like terms: 0 + -190 = -190 -190 + 11t + 16t2 = 190 + -11t + -16t2 + -190 + 11t + 16t2 Reorder the terms: -190 + 11t + 16t2 = 190 + -190 + -11t + 11t + -16t2 + 16t2 Combine like terms: 190 + -190 = 0 -190 + 11t + 16t2 = 0 + -11t + 11t + -16t2 + 16t2 -190 + 11t + 16t2 = -11t + 11t + -16t2 + 16t2 Combine like terms: -11t + 11t = 0 -190 + 11t + 16t2 = 0 + -16t2 + 16t2 -190 + 11t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -190 + 11t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -11.875 + 0.6875t + t2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + 0.6875t + 11.875 + t2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + 0.6875t + t2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + 0.6875t + t2 = 0 + 11.875 0.6875t + t2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 0.6875t + t2 = 11.875 The t term is 0.6875t. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875t + 0.1181640625 + t2 = 11.875 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875t + t2 = 11.875 + 0.1181640625 Combine like terms: 11.875 + 0.1181640625 = 11.9931640625 0.1181640625 + 0.6875t + t2 = 11.9931640625 Factor a perfect square on the left side: (t + 0.34375)(t + 0.34375) = 11.9931640625 Calculate the square root of the right side: 3.463114792 Break this problem into two subproblems by setting (t + 0.34375) equal to 3.463114792 and -3.463114792.Subproblem 1
t + 0.34375 = 3.463114792 Simplifying t + 0.34375 = 3.463114792 Reorder the terms: 0.34375 + t = 3.463114792 Solving 0.34375 + t = 3.463114792 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = 3.463114792 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = 3.463114792 + -0.34375 t = 3.463114792 + -0.34375 Combine like terms: 3.463114792 + -0.34375 = 3.119364792 t = 3.119364792 Simplifying t = 3.119364792Subproblem 2
t + 0.34375 = -3.463114792 Simplifying t + 0.34375 = -3.463114792 Reorder the terms: 0.34375 + t = -3.463114792 Solving 0.34375 + t = -3.463114792 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + t = -3.463114792 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = -3.463114792 + -0.34375 t = -3.463114792 + -0.34375 Combine like terms: -3.463114792 + -0.34375 = -3.806864792 t = -3.806864792 Simplifying t = -3.806864792Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.119364792, -3.806864792}
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