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Simplifying 4.905t2 + 5.13t + -16 = 0 Reorder the terms: -16 + 5.13t + 4.905t2 = 0 Solving -16 + 5.13t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -3.261977574 + 1.04587156t + t2 = 0 Move the constant term to the right: Add '3.261977574' to each side of the equation. -3.261977574 + 1.04587156t + 3.261977574 + t2 = 0 + 3.261977574 Reorder the terms: -3.261977574 + 3.261977574 + 1.04587156t + t2 = 0 + 3.261977574 Combine like terms: -3.261977574 + 3.261977574 = 0.000000000 0.000000000 + 1.04587156t + t2 = 0 + 3.261977574 1.04587156t + t2 = 0 + 3.261977574 Combine like terms: 0 + 3.261977574 = 3.261977574 1.04587156t + t2 = 3.261977574 The t term is 1.04587156t. Take half its coefficient (0.52293578). Square it (0.2734618300) and add it to both sides. Add '0.2734618300' to each side of the equation. 1.04587156t + 0.2734618300 + t2 = 3.261977574 + 0.2734618300 Reorder the terms: 0.2734618300 + 1.04587156t + t2 = 3.261977574 + 0.2734618300 Combine like terms: 3.261977574 + 0.2734618300 = 3.535439404 0.2734618300 + 1.04587156t + t2 = 3.535439404 Factor a perfect square on the left side: (t + 0.52293578)(t + 0.52293578) = 3.535439404 Calculate the square root of the right side: 1.880276417 Break this problem into two subproblems by setting (t + 0.52293578) equal to 1.880276417 and -1.880276417.Subproblem 1
t + 0.52293578 = 1.880276417 Simplifying t + 0.52293578 = 1.880276417 Reorder the terms: 0.52293578 + t = 1.880276417 Solving 0.52293578 + t = 1.880276417 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.52293578' to each side of the equation. 0.52293578 + -0.52293578 + t = 1.880276417 + -0.52293578 Combine like terms: 0.52293578 + -0.52293578 = 0.00000000 0.00000000 + t = 1.880276417 + -0.52293578 t = 1.880276417 + -0.52293578 Combine like terms: 1.880276417 + -0.52293578 = 1.357340637 t = 1.357340637 Simplifying t = 1.357340637Subproblem 2
t + 0.52293578 = -1.880276417 Simplifying t + 0.52293578 = -1.880276417 Reorder the terms: 0.52293578 + t = -1.880276417 Solving 0.52293578 + t = -1.880276417 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.52293578' to each side of the equation. 0.52293578 + -0.52293578 + t = -1.880276417 + -0.52293578 Combine like terms: 0.52293578 + -0.52293578 = 0.00000000 0.00000000 + t = -1.880276417 + -0.52293578 t = -1.880276417 + -0.52293578 Combine like terms: -1.880276417 + -0.52293578 = -2.403212197 t = -2.403212197 Simplifying t = -2.403212197Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.357340637, -2.403212197}
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