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Simplifying 10 = 12t + -0.02t2 Solving 10 = 12t + -0.02t2 Solving for variable 't'. Reorder the terms: 10 + -12t + 0.02t2 = 12t + -12t + -0.02t2 + 0.02t2 Combine like terms: 12t + -12t = 0 10 + -12t + 0.02t2 = 0 + -0.02t2 + 0.02t2 10 + -12t + 0.02t2 = -0.02t2 + 0.02t2 Combine like terms: -0.02t2 + 0.02t2 = 0.00 10 + -12t + 0.02t2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 500 + -600t + t2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -600t + -500 + t2 = 0 + -500 Reorder the terms: 500 + -500 + -600t + t2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -600t + t2 = 0 + -500 -600t + t2 = 0 + -500 Combine like terms: 0 + -500 = -500 -600t + t2 = -500 The t term is -600t. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600t + 90000 + t2 = -500 + 90000 Reorder the terms: 90000 + -600t + t2 = -500 + 90000 Combine like terms: -500 + 90000 = 89500 90000 + -600t + t2 = 89500 Factor a perfect square on the left side: (t + -300)(t + -300) = 89500 Calculate the square root of the right side: 299.165506033 Break this problem into two subproblems by setting (t + -300) equal to 299.165506033 and -299.165506033.Subproblem 1
t + -300 = 299.165506033 Simplifying t + -300 = 299.165506033 Reorder the terms: -300 + t = 299.165506033 Solving -300 + t = 299.165506033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + t = 299.165506033 + 300 Combine like terms: -300 + 300 = 0 0 + t = 299.165506033 + 300 t = 299.165506033 + 300 Combine like terms: 299.165506033 + 300 = 599.165506033 t = 599.165506033 Simplifying t = 599.165506033Subproblem 2
t + -300 = -299.165506033 Simplifying t + -300 = -299.165506033 Reorder the terms: -300 + t = -299.165506033 Solving -300 + t = -299.165506033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + t = -299.165506033 + 300 Combine like terms: -300 + 300 = 0 0 + t = -299.165506033 + 300 t = -299.165506033 + 300 Combine like terms: -299.165506033 + 300 = 0.834493967 t = 0.834493967 Simplifying t = 0.834493967Solution
The solution to the problem is based on the solutions from the subproblems. t = {599.165506033, 0.834493967}
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