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Simplifying 0.0825t2 + -0.888t + 1.721 = 0 Reorder the terms: 1.721 + -0.888t + 0.0825t2 = 0 Solving 1.721 + -0.888t + 0.0825t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 20.86060606 + -10.76363636t + t2 = 0 Move the constant term to the right: Add '-20.86060606' to each side of the equation. 20.86060606 + -10.76363636t + -20.86060606 + t2 = 0 + -20.86060606 Reorder the terms: 20.86060606 + -20.86060606 + -10.76363636t + t2 = 0 + -20.86060606 Combine like terms: 20.86060606 + -20.86060606 = 0.00000000 0.00000000 + -10.76363636t + t2 = 0 + -20.86060606 -10.76363636t + t2 = 0 + -20.86060606 Combine like terms: 0 + -20.86060606 = -20.86060606 -10.76363636t + t2 = -20.86060606 The t term is -10.76363636t. Take half its coefficient (-5.38181818). Square it (28.96396692) and add it to both sides. Add '28.96396692' to each side of the equation. -10.76363636t + 28.96396692 + t2 = -20.86060606 + 28.96396692 Reorder the terms: 28.96396692 + -10.76363636t + t2 = -20.86060606 + 28.96396692 Combine like terms: -20.86060606 + 28.96396692 = 8.10336086 28.96396692 + -10.76363636t + t2 = 8.10336086 Factor a perfect square on the left side: (t + -5.38181818)(t + -5.38181818) = 8.10336086 Calculate the square root of the right side: 2.846640276 Break this problem into two subproblems by setting (t + -5.38181818) equal to 2.846640276 and -2.846640276.Subproblem 1
t + -5.38181818 = 2.846640276 Simplifying t + -5.38181818 = 2.846640276 Reorder the terms: -5.38181818 + t = 2.846640276 Solving -5.38181818 + t = 2.846640276 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.38181818' to each side of the equation. -5.38181818 + 5.38181818 + t = 2.846640276 + 5.38181818 Combine like terms: -5.38181818 + 5.38181818 = 0.00000000 0.00000000 + t = 2.846640276 + 5.38181818 t = 2.846640276 + 5.38181818 Combine like terms: 2.846640276 + 5.38181818 = 8.228458456 t = 8.228458456 Simplifying t = 8.228458456Subproblem 2
t + -5.38181818 = -2.846640276 Simplifying t + -5.38181818 = -2.846640276 Reorder the terms: -5.38181818 + t = -2.846640276 Solving -5.38181818 + t = -2.846640276 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.38181818' to each side of the equation. -5.38181818 + 5.38181818 + t = -2.846640276 + 5.38181818 Combine like terms: -5.38181818 + 5.38181818 = 0.00000000 0.00000000 + t = -2.846640276 + 5.38181818 t = -2.846640276 + 5.38181818 Combine like terms: -2.846640276 + 5.38181818 = 2.535177904 t = 2.535177904 Simplifying t = 2.535177904Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.228458456, 2.535177904}
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