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Simplifying 4.9t2 + t = 3 Reorder the terms: t + 4.9t2 = 3 Solving t + 4.9t2 = 3 Solving for variable 't'. Reorder the terms: -3 + t + 4.9t2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.612244898 + 0.2040816327t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + 0.2040816327t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + 0.2040816327t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + 0.2040816327t + t2 = 0 + 0.612244898 0.2040816327t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 0.2040816327t + t2 = 0.612244898 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2040816327t + 0.25 + t2 = 0.612244898 + 0.25 Reorder the terms: 0.25 + 0.2040816327t + t2 = 0.612244898 + 0.25 Combine like terms: 0.612244898 + 0.25 = 0.862244898 0.25 + 0.2040816327t + t2 = 0.862244898 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.862244898 Calculate the square root of the right side: 0.928571429 Break this problem into two subproblems by setting (t + 0.5) equal to 0.928571429 and -0.928571429.Subproblem 1
t + 0.5 = 0.928571429 Simplifying t + 0.5 = 0.928571429 Reorder the terms: 0.5 + t = 0.928571429 Solving 0.5 + t = 0.928571429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.928571429 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.928571429 + -0.5 t = 0.928571429 + -0.5 Combine like terms: 0.928571429 + -0.5 = 0.428571429 t = 0.428571429 Simplifying t = 0.428571429Subproblem 2
t + 0.5 = -0.928571429 Simplifying t + 0.5 = -0.928571429 Reorder the terms: 0.5 + t = -0.928571429 Solving 0.5 + t = -0.928571429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.928571429 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.928571429 + -0.5 t = -0.928571429 + -0.5 Combine like terms: -0.928571429 + -0.5 = -1.428571429 t = -1.428571429 Simplifying t = -1.428571429Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.428571429, -1.428571429}
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