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Simplifying 8 = 19t + -4.9t2 Solving 8 = 19t + -4.9t2 Solving for variable 't'. Reorder the terms: 8 + -19t + 4.9t2 = 19t + -19t + -4.9t2 + 4.9t2 Combine like terms: 19t + -19t = 0 8 + -19t + 4.9t2 = 0 + -4.9t2 + 4.9t2 8 + -19t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 8 + -19t + 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'. 1.632653061 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '-1.632653061' to each side of the equation. 1.632653061 + -3.87755102t + -1.632653061 + t2 = 0 + -1.632653061 Reorder the terms: 1.632653061 + -1.632653061 + -3.87755102t + t2 = 0 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + -3.87755102t + t2 = 0 + -1.632653061 -3.87755102t + t2 = 0 + -1.632653061 Combine like terms: 0 + -1.632653061 = -1.632653061 -3.87755102t + t2 = -1.632653061 The t term is -3.87755102t. Take half its coefficient (-1.93877551). Square it (3.758850478) and add it to both sides. Add '3.758850478' to each side of the equation. -3.87755102t + 3.758850478 + t2 = -1.632653061 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = -1.632653061 + 3.758850478 Combine like terms: -1.632653061 + 3.758850478 = 2.126197417 3.758850478 + -3.87755102t + t2 = 2.126197417 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 2.126197417 Calculate the square root of the right side: 1.458148627 Break this problem into two subproblems by setting (t + -1.93877551) equal to 1.458148627 and -1.458148627.Subproblem 1
t + -1.93877551 = 1.458148627 Simplifying t + -1.93877551 = 1.458148627 Reorder the terms: -1.93877551 + t = 1.458148627 Solving -1.93877551 + t = 1.458148627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + t = 1.458148627 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 1.458148627 + 1.93877551 t = 1.458148627 + 1.93877551 Combine like terms: 1.458148627 + 1.93877551 = 3.396924137 t = 3.396924137 Simplifying t = 3.396924137Subproblem 2
t + -1.93877551 = -1.458148627 Simplifying t + -1.93877551 = -1.458148627 Reorder the terms: -1.93877551 + t = -1.458148627 Solving -1.93877551 + t = -1.458148627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + t = -1.458148627 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -1.458148627 + 1.93877551 t = -1.458148627 + 1.93877551 Combine like terms: -1.458148627 + 1.93877551 = 0.480626883 t = 0.480626883 Simplifying t = 0.480626883Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.396924137, 0.480626883}
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