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Simplifying 3t2 + -120t + 800 = 0 Reorder the terms: 800 + -120t + 3t2 = 0 Solving 800 + -120t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 266.6666667 + -40t + t2 = 0 Move the constant term to the right: Add '-266.6666667' to each side of the equation. 266.6666667 + -40t + -266.6666667 + t2 = 0 + -266.6666667 Reorder the terms: 266.6666667 + -266.6666667 + -40t + t2 = 0 + -266.6666667 Combine like terms: 266.6666667 + -266.6666667 = 0.0000000 0.0000000 + -40t + t2 = 0 + -266.6666667 -40t + t2 = 0 + -266.6666667 Combine like terms: 0 + -266.6666667 = -266.6666667 -40t + t2 = -266.6666667 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = -266.6666667 + 400 Reorder the terms: 400 + -40t + t2 = -266.6666667 + 400 Combine like terms: -266.6666667 + 400 = 133.3333333 400 + -40t + t2 = 133.3333333 Factor a perfect square on the left side: (t + -20)(t + -20) = 133.3333333 Calculate the square root of the right side: 11.547005382 Break this problem into two subproblems by setting (t + -20) equal to 11.547005382 and -11.547005382.Subproblem 1
t + -20 = 11.547005382 Simplifying t + -20 = 11.547005382 Reorder the terms: -20 + t = 11.547005382 Solving -20 + t = 11.547005382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 11.547005382 + 20 Combine like terms: -20 + 20 = 0 0 + t = 11.547005382 + 20 t = 11.547005382 + 20 Combine like terms: 11.547005382 + 20 = 31.547005382 t = 31.547005382 Simplifying t = 31.547005382Subproblem 2
t + -20 = -11.547005382 Simplifying t + -20 = -11.547005382 Reorder the terms: -20 + t = -11.547005382 Solving -20 + t = -11.547005382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -11.547005382 + 20 Combine like terms: -20 + 20 = 0 0 + t = -11.547005382 + 20 t = -11.547005382 + 20 Combine like terms: -11.547005382 + 20 = 8.452994618 t = 8.452994618 Simplifying t = 8.452994618Solution
The solution to the problem is based on the solutions from the subproblems. t = {31.547005382, 8.452994618}
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