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Simplifying 0 = 49 + -2t + -5t2 Solving 0 = 49 + -2t + -5t2 Solving for variable 't'. Combine like terms: 0 + -49 = -49 -49 + 2t + 5t2 = 49 + -2t + -5t2 + -49 + 2t + 5t2 Reorder the terms: -49 + 2t + 5t2 = 49 + -49 + -2t + 2t + -5t2 + 5t2 Combine like terms: 49 + -49 = 0 -49 + 2t + 5t2 = 0 + -2t + 2t + -5t2 + 5t2 -49 + 2t + 5t2 = -2t + 2t + -5t2 + 5t2 Combine like terms: -2t + 2t = 0 -49 + 2t + 5t2 = 0 + -5t2 + 5t2 -49 + 2t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -49 + 2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.8 + 0.4t + t2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + 0.4t + 9.8 + t2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + 0.4t + t2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + 0.4t + t2 = 0 + 9.8 0.4t + t2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 0.4t + t2 = 9.8 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 9.8 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 9.8 + 0.04 Combine like terms: 9.8 + 0.04 = 9.84 0.04 + 0.4t + t2 = 9.84 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 9.84 Calculate the square root of the right side: 3.136877428 Break this problem into two subproblems by setting (t + 0.2) equal to 3.136877428 and -3.136877428.Subproblem 1
t + 0.2 = 3.136877428 Simplifying t + 0.2 = 3.136877428 Reorder the terms: 0.2 + t = 3.136877428 Solving 0.2 + t = 3.136877428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 3.136877428 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 3.136877428 + -0.2 t = 3.136877428 + -0.2 Combine like terms: 3.136877428 + -0.2 = 2.936877428 t = 2.936877428 Simplifying t = 2.936877428Subproblem 2
t + 0.2 = -3.136877428 Simplifying t + 0.2 = -3.136877428 Reorder the terms: 0.2 + t = -3.136877428 Solving 0.2 + t = -3.136877428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -3.136877428 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -3.136877428 + -0.2 t = -3.136877428 + -0.2 Combine like terms: -3.136877428 + -0.2 = -3.336877428 t = -3.336877428 Simplifying t = -3.336877428Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.936877428, -3.336877428}
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