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Simplifying 4.9t2 + -19t + -7 = 0 Reorder the terms: -7 + -19t + 4.9t2 = 0 Solving -7 + -19t + 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'. -1.428571429 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -3.87755102t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -3.87755102t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -3.87755102t + t2 = 0 + 1.428571429 -3.87755102t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -3.87755102t + t2 = 1.428571429 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 = 1.428571429 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = 1.428571429 + 3.758850478 Combine like terms: 1.428571429 + 3.758850478 = 5.187421907 3.758850478 + -3.87755102t + t2 = 5.187421907 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 5.187421907 Calculate the square root of the right side: 2.277591251 Break this problem into two subproblems by setting (t + -1.93877551) equal to 2.277591251 and -2.277591251.Subproblem 1
t + -1.93877551 = 2.277591251 Simplifying t + -1.93877551 = 2.277591251 Reorder the terms: -1.93877551 + t = 2.277591251 Solving -1.93877551 + t = 2.277591251 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 = 2.277591251 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 2.277591251 + 1.93877551 t = 2.277591251 + 1.93877551 Combine like terms: 2.277591251 + 1.93877551 = 4.216366761 t = 4.216366761 Simplifying t = 4.216366761Subproblem 2
t + -1.93877551 = -2.277591251 Simplifying t + -1.93877551 = -2.277591251 Reorder the terms: -1.93877551 + t = -2.277591251 Solving -1.93877551 + t = -2.277591251 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 = -2.277591251 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -2.277591251 + 1.93877551 t = -2.277591251 + 1.93877551 Combine like terms: -2.277591251 + 1.93877551 = -0.338815741 t = -0.338815741 Simplifying t = -0.338815741Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.216366761, -0.338815741}
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