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Simplifying 0 = 0.0855t2 + -0.906t + 1.734 Reorder the terms: 0 = 1.734 + -0.906t + 0.0855t2 Solving 0 = 1.734 + -0.906t + 0.0855t2 Solving for variable 't'. Combine like terms: 0 + -1.734 = -1.734 -1.734 + 0.906t + -0.0855t2 = 1.734 + -0.906t + 0.0855t2 + -1.734 + 0.906t + -0.0855t2 Reorder the terms: -1.734 + 0.906t + -0.0855t2 = 1.734 + -1.734 + -0.906t + 0.906t + 0.0855t2 + -0.0855t2 Combine like terms: 1.734 + -1.734 = 0.000 -1.734 + 0.906t + -0.0855t2 = 0.000 + -0.906t + 0.906t + 0.0855t2 + -0.0855t2 -1.734 + 0.906t + -0.0855t2 = -0.906t + 0.906t + 0.0855t2 + -0.0855t2 Combine like terms: -0.906t + 0.906t = 0.000 -1.734 + 0.906t + -0.0855t2 = 0.000 + 0.0855t2 + -0.0855t2 -1.734 + 0.906t + -0.0855t2 = 0.0855t2 + -0.0855t2 Combine like terms: 0.0855t2 + -0.0855t2 = 0.0000 -1.734 + 0.906t + -0.0855t2 = 0.0000 Begin completing the square. Divide all terms by -0.0855 the coefficient of the squared term: Divide each side by '-0.0855'. 20.28070175 + -10.59649123t + t2 = 0 Move the constant term to the right: Add '-20.28070175' to each side of the equation. 20.28070175 + -10.59649123t + -20.28070175 + t2 = 0 + -20.28070175 Reorder the terms: 20.28070175 + -20.28070175 + -10.59649123t + t2 = 0 + -20.28070175 Combine like terms: 20.28070175 + -20.28070175 = 0.00000000 0.00000000 + -10.59649123t + t2 = 0 + -20.28070175 -10.59649123t + t2 = 0 + -20.28070175 Combine like terms: 0 + -20.28070175 = -20.28070175 -10.59649123t + t2 = -20.28070175 The t term is -10.59649123t. Take half its coefficient (-5.298245615). Square it (28.07140660) and add it to both sides. Add '28.07140660' to each side of the equation. -10.59649123t + 28.07140660 + t2 = -20.28070175 + 28.07140660 Reorder the terms: 28.07140660 + -10.59649123t + t2 = -20.28070175 + 28.07140660 Combine like terms: -20.28070175 + 28.07140660 = 7.79070485 28.07140660 + -10.59649123t + t2 = 7.79070485 Factor a perfect square on the left side: (t + -5.298245615)(t + -5.298245615) = 7.79070485 Calculate the square root of the right side: 2.791183414 Break this problem into two subproblems by setting (t + -5.298245615) equal to 2.791183414 and -2.791183414.Subproblem 1
t + -5.298245615 = 2.791183414 Simplifying t + -5.298245615 = 2.791183414 Reorder the terms: -5.298245615 + t = 2.791183414 Solving -5.298245615 + t = 2.791183414 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.298245615' to each side of the equation. -5.298245615 + 5.298245615 + t = 2.791183414 + 5.298245615 Combine like terms: -5.298245615 + 5.298245615 = 0.000000000 0.000000000 + t = 2.791183414 + 5.298245615 t = 2.791183414 + 5.298245615 Combine like terms: 2.791183414 + 5.298245615 = 8.089429029 t = 8.089429029 Simplifying t = 8.089429029Subproblem 2
t + -5.298245615 = -2.791183414 Simplifying t + -5.298245615 = -2.791183414 Reorder the terms: -5.298245615 + t = -2.791183414 Solving -5.298245615 + t = -2.791183414 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.298245615' to each side of the equation. -5.298245615 + 5.298245615 + t = -2.791183414 + 5.298245615 Combine like terms: -5.298245615 + 5.298245615 = 0.000000000 0.000000000 + t = -2.791183414 + 5.298245615 t = -2.791183414 + 5.298245615 Combine like terms: -2.791183414 + 5.298245615 = 2.507062201 t = 2.507062201 Simplifying t = 2.507062201Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.089429029, 2.507062201}
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