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Simplifying 0 = 4.9t2 + -25t + 3 Reorder the terms: 0 = 3 + -25t + 4.9t2 Solving 0 = 3 + -25t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + 25t + -4.9t2 = 3 + -25t + 4.9t2 + -3 + 25t + -4.9t2 Reorder the terms: -3 + 25t + -4.9t2 = 3 + -3 + -25t + 25t + 4.9t2 + -4.9t2 Combine like terms: 3 + -3 = 0 -3 + 25t + -4.9t2 = 0 + -25t + 25t + 4.9t2 + -4.9t2 -3 + 25t + -4.9t2 = -25t + 25t + 4.9t2 + -4.9t2 Combine like terms: -25t + 25t = 0 -3 + 25t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -3 + 25t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -3 + 25t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.612244898 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + -5.102040816t + -0.612244898 + t2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + -5.102040816t + t2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + -0.612244898 -5.102040816t + t2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 -5.102040816t + t2 = -0.612244898 The t term is -5.102040816t. Take half its coefficient (-2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. -5.102040816t + 6.507705122 + t2 = -0.612244898 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = -0.612244898 + 6.507705122 Combine like terms: -0.612244898 + 6.507705122 = 5.895460224 6.507705122 + -5.102040816t + t2 = 5.895460224 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 5.895460224 Calculate the square root of the right side: 2.428056882 Break this problem into two subproblems by setting (t + -2.551020408) equal to 2.428056882 and -2.428056882.Subproblem 1
t + -2.551020408 = 2.428056882 Simplifying t + -2.551020408 = 2.428056882 Reorder the terms: -2.551020408 + t = 2.428056882 Solving -2.551020408 + t = 2.428056882 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = 2.428056882 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 2.428056882 + 2.551020408 t = 2.428056882 + 2.551020408 Combine like terms: 2.428056882 + 2.551020408 = 4.97907729 t = 4.97907729 Simplifying t = 4.97907729Subproblem 2
t + -2.551020408 = -2.428056882 Simplifying t + -2.551020408 = -2.428056882 Reorder the terms: -2.551020408 + t = -2.428056882 Solving -2.551020408 + t = -2.428056882 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.551020408' to each side of the equation. -2.551020408 + 2.551020408 + t = -2.428056882 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -2.428056882 + 2.551020408 t = -2.428056882 + 2.551020408 Combine like terms: -2.428056882 + 2.551020408 = 0.122963526 t = 0.122963526 Simplifying t = 0.122963526Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.97907729, 0.122963526}
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