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Simplifying 0 = -4.9t2 + 19t + -4 Reorder the terms: 0 = -4 + 19t + -4.9t2 Solving 0 = -4 + 19t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 4 = 4 4 + -19t + 4.9t2 = -4 + 19t + -4.9t2 + 4 + -19t + 4.9t2 Reorder the terms: 4 + -19t + 4.9t2 = -4 + 4 + 19t + -19t + -4.9t2 + 4.9t2 Combine like terms: -4 + 4 = 0 4 + -19t + 4.9t2 = 0 + 19t + -19t + -4.9t2 + 4.9t2 4 + -19t + 4.9t2 = 19t + -19t + -4.9t2 + 4.9t2 Combine like terms: 19t + -19t = 0 4 + -19t + 4.9t2 = 0 + -4.9t2 + 4.9t2 4 + -19t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 4 + -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'. 0.8163265306 + -3.87755102t + t2 = 0 Move the constant term to the right: Add '-0.8163265306' to each side of the equation. 0.8163265306 + -3.87755102t + -0.8163265306 + t2 = 0 + -0.8163265306 Reorder the terms: 0.8163265306 + -0.8163265306 + -3.87755102t + t2 = 0 + -0.8163265306 Combine like terms: 0.8163265306 + -0.8163265306 = 0.0000000000 0.0000000000 + -3.87755102t + t2 = 0 + -0.8163265306 -3.87755102t + t2 = 0 + -0.8163265306 Combine like terms: 0 + -0.8163265306 = -0.8163265306 -3.87755102t + t2 = -0.8163265306 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 = -0.8163265306 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102t + t2 = -0.8163265306 + 3.758850478 Combine like terms: -0.8163265306 + 3.758850478 = 2.9425239474 3.758850478 + -3.87755102t + t2 = 2.9425239474 Factor a perfect square on the left side: (t + -1.93877551)(t + -1.93877551) = 2.9425239474 Calculate the square root of the right side: 1.71537866 Break this problem into two subproblems by setting (t + -1.93877551) equal to 1.71537866 and -1.71537866.Subproblem 1
t + -1.93877551 = 1.71537866 Simplifying t + -1.93877551 = 1.71537866 Reorder the terms: -1.93877551 + t = 1.71537866 Solving -1.93877551 + t = 1.71537866 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 = 1.71537866 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = 1.71537866 + 1.93877551 t = 1.71537866 + 1.93877551 Combine like terms: 1.71537866 + 1.93877551 = 3.65415417 t = 3.65415417 Simplifying t = 3.65415417Subproblem 2
t + -1.93877551 = -1.71537866 Simplifying t + -1.93877551 = -1.71537866 Reorder the terms: -1.93877551 + t = -1.71537866 Solving -1.93877551 + t = -1.71537866 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 = -1.71537866 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + t = -1.71537866 + 1.93877551 t = -1.71537866 + 1.93877551 Combine like terms: -1.71537866 + 1.93877551 = 0.22339685 t = 0.22339685 Simplifying t = 0.22339685Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.65415417, 0.22339685}
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