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Simplifying 4.9t2 + -5t + -19.6 = 0 Reorder the terms: -19.6 + -5t + 4.9t2 = 0 Solving -19.6 + -5t + 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'. -4 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.020408163t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -1.020408163t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.020408163t + t2 = 0 + 4 -1.020408163t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.020408163t + t2 = 4 The t term is -1.020408163t. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163t + 0.2603082048 + t2 = 4 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 4 + 0.2603082048 Combine like terms: 4 + 0.2603082048 = 4.2603082048 0.2603082048 + -1.020408163t + t2 = 4.2603082048 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 4.2603082048 Calculate the square root of the right side: 2.064051406 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 2.064051406 and -2.064051406.Subproblem 1
t + -0.5102040815 = 2.064051406 Simplifying t + -0.5102040815 = 2.064051406 Reorder the terms: -0.5102040815 + t = 2.064051406 Solving -0.5102040815 + t = 2.064051406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = 2.064051406 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 2.064051406 + 0.5102040815 t = 2.064051406 + 0.5102040815 Combine like terms: 2.064051406 + 0.5102040815 = 2.5742554875 t = 2.5742554875 Simplifying t = 2.5742554875Subproblem 2
t + -0.5102040815 = -2.064051406 Simplifying t + -0.5102040815 = -2.064051406 Reorder the terms: -0.5102040815 + t = -2.064051406 Solving -0.5102040815 + t = -2.064051406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = -2.064051406 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -2.064051406 + 0.5102040815 t = -2.064051406 + 0.5102040815 Combine like terms: -2.064051406 + 0.5102040815 = -1.5538473245 t = -1.5538473245 Simplifying t = -1.5538473245Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5742554875, -1.5538473245}
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