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Simplifying 4.9t2 + -24.5t + 2 = 0 Reorder the terms: 2 + -24.5t + 4.9t2 = 0 Solving 2 + -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'. 0.4081632653 + -5t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -5t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -5t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -5t + t2 = 0 + -0.4081632653 -5t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -5t + t2 = -0.4081632653 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 = -0.4081632653 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -0.4081632653 + 6.25 Combine like terms: -0.4081632653 + 6.25 = 5.8418367347 6.25 + -5t + t2 = 5.8418367347 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 5.8418367347 Calculate the square root of the right side: 2.416989188 Break this problem into two subproblems by setting (t + -2.5) equal to 2.416989188 and -2.416989188.Subproblem 1
t + -2.5 = 2.416989188 Simplifying t + -2.5 = 2.416989188 Reorder the terms: -2.5 + t = 2.416989188 Solving -2.5 + t = 2.416989188 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 = 2.416989188 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.416989188 + 2.5 t = 2.416989188 + 2.5 Combine like terms: 2.416989188 + 2.5 = 4.916989188 t = 4.916989188 Simplifying t = 4.916989188Subproblem 2
t + -2.5 = -2.416989188 Simplifying t + -2.5 = -2.416989188 Reorder the terms: -2.5 + t = -2.416989188 Solving -2.5 + t = -2.416989188 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 = -2.416989188 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.416989188 + 2.5 t = -2.416989188 + 2.5 Combine like terms: -2.416989188 + 2.5 = 0.083010812 t = 0.083010812 Simplifying t = 0.083010812Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.916989188, 0.083010812}
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