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Simplifying 4.9t2 + 9 = 19t Reorder the terms: 9 + 4.9t2 = 19t Solving 9 + 4.9t2 = 19t Solving for variable 't'. Reorder the terms: 9 + -19t + 4.9t2 = 19t + -19t Combine like terms: 19t + -19t = 0 9 + -19t + 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'. 1.836734694 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '-1.836734694' to each side of the equation. 1.836734694 + -3.87755102t + -1.836734694 + t2 = 0 + -1.836734694 Reorder the terms: 1.836734694 + -1.836734694 + -3.87755102t + t2 = 0 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + -3.87755102t + t2 = 0 + -1.836734694 -3.87755102t + t2 = 0 + -1.836734694 Combine like terms: 0 + -1.836734694 = -1.836734694 -3.87755102t + t2 = -1.836734694 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 = -1.836734694 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = -1.836734694 + 3.758850478 Combine like terms: -1.836734694 + 3.758850478 = 1.922115784 3.758850478 + -3.87755102t + t2 = 1.922115784 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 1.922115784 Calculate the square root of the right side: 1.386403904 Break this problem into two subproblems by setting (t + -1.93877551) equal to 1.386403904 and -1.386403904.Subproblem 1
t + -1.93877551 = 1.386403904 Simplifying t + -1.93877551 = 1.386403904 Reorder the terms: -1.93877551 + t = 1.386403904 Solving -1.93877551 + t = 1.386403904 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 = 1.386403904 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 1.386403904 + 1.93877551 t = 1.386403904 + 1.93877551 Combine like terms: 1.386403904 + 1.93877551 = 3.325179414 t = 3.325179414 Simplifying t = 3.325179414Subproblem 2
t + -1.93877551 = -1.386403904 Simplifying t + -1.93877551 = -1.386403904 Reorder the terms: -1.93877551 + t = -1.386403904 Solving -1.93877551 + t = -1.386403904 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 = -1.386403904 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -1.386403904 + 1.93877551 t = -1.386403904 + 1.93877551 Combine like terms: -1.386403904 + 1.93877551 = 0.552371606 t = 0.552371606 Simplifying t = 0.552371606Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.325179414, 0.552371606}
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