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Simplifying -0.934 = -1.09t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 -0.934 = -1.09t + -4.9t2 Solving -0.934 = -1.09t + -4.9t2 Solving for variable 't'. Reorder the terms: -0.934 + 1.09t + 4.9t2 = -1.09t + 1.09t + -4.9t2 + 4.9t2 Combine like terms: -1.09t + 1.09t = 0.00 -0.934 + 1.09t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -0.934 + 1.09t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.934 + 1.09t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.1906122449 + 0.2224489796t + t2 = 0 Move the constant term to the right: Add '0.1906122449' to each side of the equation. -0.1906122449 + 0.2224489796t + 0.1906122449 + t2 = 0 + 0.1906122449 Reorder the terms: -0.1906122449 + 0.1906122449 + 0.2224489796t + t2 = 0 + 0.1906122449 Combine like terms: -0.1906122449 + 0.1906122449 = 0.0000000000 0.0000000000 + 0.2224489796t + t2 = 0 + 0.1906122449 0.2224489796t + t2 = 0 + 0.1906122449 Combine like terms: 0 + 0.1906122449 = 0.1906122449 0.2224489796t + t2 = 0.1906122449 The t term is 0.2224489796t. Take half its coefficient (0.1112244898). Square it (0.01237088713) and add it to both sides. Add '0.01237088713' to each side of the equation. 0.2224489796t + 0.01237088713 + t2 = 0.1906122449 + 0.01237088713 Reorder the terms: 0.01237088713 + 0.2224489796t + t2 = 0.1906122449 + 0.01237088713 Combine like terms: 0.1906122449 + 0.01237088713 = 0.20298313203 0.01237088713 + 0.2224489796t + t2 = 0.20298313203 Factor a perfect square on the left side: (t + 0.1112244898)(t + 0.1112244898) = 0.20298313203 Calculate the square root of the right side: 0.450536494 Break this problem into two subproblems by setting (t + 0.1112244898) equal to 0.450536494 and -0.450536494.Subproblem 1
t + 0.1112244898 = 0.450536494 Simplifying t + 0.1112244898 = 0.450536494 Reorder the terms: 0.1112244898 + t = 0.450536494 Solving 0.1112244898 + t = 0.450536494 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1112244898' to each side of the equation. 0.1112244898 + -0.1112244898 + t = 0.450536494 + -0.1112244898 Combine like terms: 0.1112244898 + -0.1112244898 = 0.0000000000 0.0000000000 + t = 0.450536494 + -0.1112244898 t = 0.450536494 + -0.1112244898 Combine like terms: 0.450536494 + -0.1112244898 = 0.3393120042 t = 0.3393120042 Simplifying t = 0.3393120042Subproblem 2
t + 0.1112244898 = -0.450536494 Simplifying t + 0.1112244898 = -0.450536494 Reorder the terms: 0.1112244898 + t = -0.450536494 Solving 0.1112244898 + t = -0.450536494 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1112244898' to each side of the equation. 0.1112244898 + -0.1112244898 + t = -0.450536494 + -0.1112244898 Combine like terms: 0.1112244898 + -0.1112244898 = 0.0000000000 0.0000000000 + t = -0.450536494 + -0.1112244898 t = -0.450536494 + -0.1112244898 Combine like terms: -0.450536494 + -0.1112244898 = -0.5617609838 t = -0.5617609838 Simplifying t = -0.5617609838Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3393120042, -0.5617609838}
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