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Simplifying 11t + 4.905t2 = 2 Solving 11t + 4.905t2 = 2 Solving for variable 't'. Reorder the terms: -2 + 11t + 4.905t2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 11t + 4.905t2 = 0 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -0.4077471967 + 2.242609582t + t2 = 0 Move the constant term to the right: Add '0.4077471967' to each side of the equation. -0.4077471967 + 2.242609582t + 0.4077471967 + t2 = 0 + 0.4077471967 Reorder the terms: -0.4077471967 + 0.4077471967 + 2.242609582t + t2 = 0 + 0.4077471967 Combine like terms: -0.4077471967 + 0.4077471967 = 0.0000000000 0.0000000000 + 2.242609582t + t2 = 0 + 0.4077471967 2.242609582t + t2 = 0 + 0.4077471967 Combine like terms: 0 + 0.4077471967 = 0.4077471967 2.242609582t + t2 = 0.4077471967 The t term is 2.242609582t. Take half its coefficient (1.121304791). Square it (1.257324434) and add it to both sides. Add '1.257324434' to each side of the equation. 2.242609582t + 1.257324434 + t2 = 0.4077471967 + 1.257324434 Reorder the terms: 1.257324434 + 2.242609582t + t2 = 0.4077471967 + 1.257324434 Combine like terms: 0.4077471967 + 1.257324434 = 1.6650716307 1.257324434 + 2.242609582t + t2 = 1.6650716307 Factor a perfect square on the left side: (t + 1.121304791)(t + 1.121304791) = 1.6650716307 Calculate the square root of the right side: 1.290376546 Break this problem into two subproblems by setting (t + 1.121304791) equal to 1.290376546 and -1.290376546.Subproblem 1
t + 1.121304791 = 1.290376546 Simplifying t + 1.121304791 = 1.290376546 Reorder the terms: 1.121304791 + t = 1.290376546 Solving 1.121304791 + t = 1.290376546 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.121304791' to each side of the equation. 1.121304791 + -1.121304791 + t = 1.290376546 + -1.121304791 Combine like terms: 1.121304791 + -1.121304791 = 0.000000000 0.000000000 + t = 1.290376546 + -1.121304791 t = 1.290376546 + -1.121304791 Combine like terms: 1.290376546 + -1.121304791 = 0.169071755 t = 0.169071755 Simplifying t = 0.169071755Subproblem 2
t + 1.121304791 = -1.290376546 Simplifying t + 1.121304791 = -1.290376546 Reorder the terms: 1.121304791 + t = -1.290376546 Solving 1.121304791 + t = -1.290376546 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.121304791' to each side of the equation. 1.121304791 + -1.121304791 + t = -1.290376546 + -1.121304791 Combine like terms: 1.121304791 + -1.121304791 = 0.000000000 0.000000000 + t = -1.290376546 + -1.121304791 t = -1.290376546 + -1.121304791 Combine like terms: -1.290376546 + -1.121304791 = -2.411681337 t = -2.411681337 Simplifying t = -2.411681337Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.169071755, -2.411681337}
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