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Simplifying 8.87t2 + -4.9t + -4 = 0 Reorder the terms: -4 + -4.9t + 8.87t2 = 0 Solving -4 + -4.9t + 8.87t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8.87 the coefficient of the squared term: Divide each side by '8.87'. -0.4509582864 + -0.5524239008t + t2 = 0 Move the constant term to the right: Add '0.4509582864' to each side of the equation. -0.4509582864 + -0.5524239008t + 0.4509582864 + t2 = 0 + 0.4509582864 Reorder the terms: -0.4509582864 + 0.4509582864 + -0.5524239008t + t2 = 0 + 0.4509582864 Combine like terms: -0.4509582864 + 0.4509582864 = 0.0000000000 0.0000000000 + -0.5524239008t + t2 = 0 + 0.4509582864 -0.5524239008t + t2 = 0 + 0.4509582864 Combine like terms: 0 + 0.4509582864 = 0.4509582864 -0.5524239008t + t2 = 0.4509582864 The t term is -0.5524239008t. Take half its coefficient (-0.2762119504). Square it (0.07629304154) and add it to both sides. Add '0.07629304154' to each side of the equation. -0.5524239008t + 0.07629304154 + t2 = 0.4509582864 + 0.07629304154 Reorder the terms: 0.07629304154 + -0.5524239008t + t2 = 0.4509582864 + 0.07629304154 Combine like terms: 0.4509582864 + 0.07629304154 = 0.52725132794 0.07629304154 + -0.5524239008t + t2 = 0.52725132794 Factor a perfect square on the left side: (t + -0.2762119504)(t + -0.2762119504) = 0.52725132794 Calculate the square root of the right side: 0.726120739 Break this problem into two subproblems by setting (t + -0.2762119504) equal to 0.726120739 and -0.726120739.Subproblem 1
t + -0.2762119504 = 0.726120739 Simplifying t + -0.2762119504 = 0.726120739 Reorder the terms: -0.2762119504 + t = 0.726120739 Solving -0.2762119504 + t = 0.726120739 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2762119504' to each side of the equation. -0.2762119504 + 0.2762119504 + t = 0.726120739 + 0.2762119504 Combine like terms: -0.2762119504 + 0.2762119504 = 0.0000000000 0.0000000000 + t = 0.726120739 + 0.2762119504 t = 0.726120739 + 0.2762119504 Combine like terms: 0.726120739 + 0.2762119504 = 1.0023326894 t = 1.0023326894 Simplifying t = 1.0023326894Subproblem 2
t + -0.2762119504 = -0.726120739 Simplifying t + -0.2762119504 = -0.726120739 Reorder the terms: -0.2762119504 + t = -0.726120739 Solving -0.2762119504 + t = -0.726120739 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2762119504' to each side of the equation. -0.2762119504 + 0.2762119504 + t = -0.726120739 + 0.2762119504 Combine like terms: -0.2762119504 + 0.2762119504 = 0.0000000000 0.0000000000 + t = -0.726120739 + 0.2762119504 t = -0.726120739 + 0.2762119504 Combine like terms: -0.726120739 + 0.2762119504 = -0.4499087886 t = -0.4499087886 Simplifying t = -0.4499087886Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.0023326894, -0.4499087886}
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