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Simplifying 4.9(t2) + -24.5(t) + -3 = 0 Reorder the terms: -3 + -24.5t + 4.9t2 = 0 Solving -3 + -24.5t + 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'. -0.612244898 + -5t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -5t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -5t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -5t + t2 = 0 + 0.612244898 -5t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -5t + t2 = 0.612244898 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 0.612244898 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 0.612244898 + 6.25 Combine like terms: 0.612244898 + 6.25 = 6.862244898 6.25 + -5t + t2 = 6.862244898 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 6.862244898 Calculate the square root of the right side: 2.619588689 Break this problem into two subproblems by setting (t + -2.5) equal to 2.619588689 and -2.619588689.Subproblem 1
t + -2.5 = 2.619588689 Simplifying t + -2.5 = 2.619588689 Reorder the terms: -2.5 + t = 2.619588689 Solving -2.5 + t = 2.619588689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.619588689 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.619588689 + 2.5 t = 2.619588689 + 2.5 Combine like terms: 2.619588689 + 2.5 = 5.119588689 t = 5.119588689 Simplifying t = 5.119588689Subproblem 2
t + -2.5 = -2.619588689 Simplifying t + -2.5 = -2.619588689 Reorder the terms: -2.5 + t = -2.619588689 Solving -2.5 + t = -2.619588689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.619588689 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.619588689 + 2.5 t = -2.619588689 + 2.5 Combine like terms: -2.619588689 + 2.5 = -0.119588689 t = -0.119588689 Simplifying t = -0.119588689Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.119588689, -0.119588689}
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