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Simplifying 0 = -16t2 + -11t + 120 Reorder the terms: 0 = 120 + -11t + -16t2 Solving 0 = 120 + -11t + -16t2 Solving for variable 't'. Combine like terms: 0 + -120 = -120 -120 + 11t + 16t2 = 120 + -11t + -16t2 + -120 + 11t + 16t2 Reorder the terms: -120 + 11t + 16t2 = 120 + -120 + -11t + 11t + -16t2 + 16t2 Combine like terms: 120 + -120 = 0 -120 + 11t + 16t2 = 0 + -11t + 11t + -16t2 + 16t2 -120 + 11t + 16t2 = -11t + 11t + -16t2 + 16t2 Combine like terms: -11t + 11t = 0 -120 + 11t + 16t2 = 0 + -16t2 + 16t2 -120 + 11t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -120 + 11t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.5 + 0.6875t + t2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 0.6875t + 7.5 + t2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 0.6875t + t2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 0.6875t + t2 = 0 + 7.5 0.6875t + t2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 0.6875t + t2 = 7.5 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 = 7.5 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875t + t2 = 7.5 + 0.1181640625 Combine like terms: 7.5 + 0.1181640625 = 7.6181640625 0.1181640625 + 0.6875t + t2 = 7.6181640625 Factor a perfect square on the left side: (t + 0.34375)(t + 0.34375) = 7.6181640625 Calculate the square root of the right side: 2.760102183 Break this problem into two subproblems by setting (t + 0.34375) equal to 2.760102183 and -2.760102183.Subproblem 1
t + 0.34375 = 2.760102183 Simplifying t + 0.34375 = 2.760102183 Reorder the terms: 0.34375 + t = 2.760102183 Solving 0.34375 + t = 2.760102183 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 = 2.760102183 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = 2.760102183 + -0.34375 t = 2.760102183 + -0.34375 Combine like terms: 2.760102183 + -0.34375 = 2.416352183 t = 2.416352183 Simplifying t = 2.416352183Subproblem 2
t + 0.34375 = -2.760102183 Simplifying t + 0.34375 = -2.760102183 Reorder the terms: 0.34375 + t = -2.760102183 Solving 0.34375 + t = -2.760102183 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 = -2.760102183 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + t = -2.760102183 + -0.34375 t = -2.760102183 + -0.34375 Combine like terms: -2.760102183 + -0.34375 = -3.103852183 t = -3.103852183 Simplifying t = -3.103852183Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.416352183, -3.103852183}
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