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Simplifying 0 = 4 + t(5 + -4.9t) 0 = 4 + (5 * t + -4.9t * t) 0 = 4 + (5t + -4.9t2) Solving 0 = 4 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -5t + 4.9t2 = 4 + 5t + -4.9t2 + -4 + -5t + 4.9t2 Reorder the terms: -4 + -5t + 4.9t2 = 4 + -4 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 4 + -4 = 0 -4 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -4 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -4 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -4 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -4 + -5t + 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 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -1.020408163t + 0.8163265306 + t2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -1.020408163t + t2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -1.020408163t + t2 = 0 + 0.8163265306 -1.020408163t + t2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -1.020408163t + t2 = 0.8163265306 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 = 0.8163265306 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 0.8163265306 + 0.2603082048 Combine like terms: 0.8163265306 + 0.2603082048 = 1.0766347354 0.2603082048 + -1.020408163t + t2 = 1.0766347354 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 1.0766347354 Calculate the square root of the right side: 1.037610108 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 1.037610108 and -1.037610108.Subproblem 1
t + -0.5102040815 = 1.037610108 Simplifying t + -0.5102040815 = 1.037610108 Reorder the terms: -0.5102040815 + t = 1.037610108 Solving -0.5102040815 + t = 1.037610108 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 = 1.037610108 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 1.037610108 + 0.5102040815 t = 1.037610108 + 0.5102040815 Combine like terms: 1.037610108 + 0.5102040815 = 1.5478141895 t = 1.5478141895 Simplifying t = 1.5478141895Subproblem 2
t + -0.5102040815 = -1.037610108 Simplifying t + -0.5102040815 = -1.037610108 Reorder the terms: -0.5102040815 + t = -1.037610108 Solving -0.5102040815 + t = -1.037610108 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 = -1.037610108 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -1.037610108 + 0.5102040815 t = -1.037610108 + 0.5102040815 Combine like terms: -1.037610108 + 0.5102040815 = -0.5274060265 t = -0.5274060265 Simplifying t = -0.5274060265Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5478141895, -0.5274060265}
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