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Simplifying 4.9t2 + -16t + 3.8 = 0 Reorder the terms: 3.8 + -16t + 4.9t2 = 0 Solving 3.8 + -16t + 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'. 0.7755102041 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '-0.7755102041' to each side of the equation. 0.7755102041 + -3.265306122t + -0.7755102041 + t2 = 0 + -0.7755102041 Reorder the terms: 0.7755102041 + -0.7755102041 + -3.265306122t + t2 = 0 + -0.7755102041 Combine like terms: 0.7755102041 + -0.7755102041 = 0.0000000000 0.0000000000 + -3.265306122t + t2 = 0 + -0.7755102041 -3.265306122t + t2 = 0 + -0.7755102041 Combine like terms: 0 + -0.7755102041 = -0.7755102041 -3.265306122t + t2 = -0.7755102041 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = -0.7755102041 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = -0.7755102041 + 2.665556018 Combine like terms: -0.7755102041 + 2.665556018 = 1.8900458139 2.665556018 + -3.265306122t + t2 = 1.8900458139 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 1.8900458139 Calculate the square root of the right side: 1.374789371 Break this problem into two subproblems by setting (t + -1.632653061) equal to 1.374789371 and -1.374789371.Subproblem 1
t + -1.632653061 = 1.374789371 Simplifying t + -1.632653061 = 1.374789371 Reorder the terms: -1.632653061 + t = 1.374789371 Solving -1.632653061 + t = 1.374789371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.374789371 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.374789371 + 1.632653061 t = 1.374789371 + 1.632653061 Combine like terms: 1.374789371 + 1.632653061 = 3.007442432 t = 3.007442432 Simplifying t = 3.007442432Subproblem 2
t + -1.632653061 = -1.374789371 Simplifying t + -1.632653061 = -1.374789371 Reorder the terms: -1.632653061 + t = -1.374789371 Solving -1.632653061 + t = -1.374789371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.374789371 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.374789371 + 1.632653061 t = -1.374789371 + 1.632653061 Combine like terms: -1.374789371 + 1.632653061 = 0.25786369 t = 0.25786369 Simplifying t = 0.25786369Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.007442432, 0.25786369}
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