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Simplifying 4.9t2 + 38t + -25 = 0 Reorder the terms: -25 + 38t + 4.9t2 = 0 Solving -25 + 38t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -5.102040816 + 7.755102041t + t2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + 7.755102041t + 5.102040816 + t2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + 7.755102041t + t2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + 7.755102041t + t2 = 0 + 5.102040816 7.755102041t + t2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 7.755102041t + t2 = 5.102040816 The t term is 7.755102041t. Take half its coefficient (3.877551021). Square it (15.03540192) and add it to both sides. Add '15.03540192' to each side of the equation. 7.755102041t + 15.03540192 + t2 = 5.102040816 + 15.03540192 Reorder the terms: 15.03540192 + 7.755102041t + t2 = 5.102040816 + 15.03540192 Combine like terms: 5.102040816 + 15.03540192 = 20.137442736 15.03540192 + 7.755102041t + t2 = 20.137442736 Factor a perfect square on the left side: (t + 3.877551021)(t + 3.877551021) = 20.137442736 Calculate the square root of the right side: 4.48747621 Break this problem into two subproblems by setting (t + 3.877551021) equal to 4.48747621 and -4.48747621.Subproblem 1
t + 3.877551021 = 4.48747621 Simplifying t + 3.877551021 = 4.48747621 Reorder the terms: 3.877551021 + t = 4.48747621 Solving 3.877551021 + t = 4.48747621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.877551021' to each side of the equation. 3.877551021 + -3.877551021 + t = 4.48747621 + -3.877551021 Combine like terms: 3.877551021 + -3.877551021 = 0.000000000 0.000000000 + t = 4.48747621 + -3.877551021 t = 4.48747621 + -3.877551021 Combine like terms: 4.48747621 + -3.877551021 = 0.609925189 t = 0.609925189 Simplifying t = 0.609925189Subproblem 2
t + 3.877551021 = -4.48747621 Simplifying t + 3.877551021 = -4.48747621 Reorder the terms: 3.877551021 + t = -4.48747621 Solving 3.877551021 + t = -4.48747621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.877551021' to each side of the equation. 3.877551021 + -3.877551021 + t = -4.48747621 + -3.877551021 Combine like terms: 3.877551021 + -3.877551021 = 0.000000000 0.000000000 + t = -4.48747621 + -3.877551021 t = -4.48747621 + -3.877551021 Combine like terms: -4.48747621 + -3.877551021 = -8.365027231 t = -8.365027231 Simplifying t = -8.365027231Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.609925189, -8.365027231}
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