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Simplifying 0 = -4.9t2 + 5t + 22 Reorder the terms: 0 = 22 + 5t + -4.9t2 Solving 0 = 22 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -22 = -22 -22 + -5t + 4.9t2 = 22 + 5t + -4.9t2 + -22 + -5t + 4.9t2 Reorder the terms: -22 + -5t + 4.9t2 = 22 + -22 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 22 + -22 = 0 -22 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -22 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -22 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -22 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -22 + -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'. -4.489795918 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + -1.020408163t + 4.489795918 + t2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + -1.020408163t + t2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + -1.020408163t + t2 = 0 + 4.489795918 -1.020408163t + t2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 -1.020408163t + t2 = 4.489795918 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 = 4.489795918 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 4.489795918 + 0.2603082048 Combine like terms: 4.489795918 + 0.2603082048 = 4.7501041228 0.2603082048 + -1.020408163t + t2 = 4.7501041228 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 4.7501041228 Calculate the square root of the right side: 2.179473359 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 2.179473359 and -2.179473359.Subproblem 1
t + -0.5102040815 = 2.179473359 Simplifying t + -0.5102040815 = 2.179473359 Reorder the terms: -0.5102040815 + t = 2.179473359 Solving -0.5102040815 + t = 2.179473359 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 = 2.179473359 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 2.179473359 + 0.5102040815 t = 2.179473359 + 0.5102040815 Combine like terms: 2.179473359 + 0.5102040815 = 2.6896774405 t = 2.6896774405 Simplifying t = 2.6896774405Subproblem 2
t + -0.5102040815 = -2.179473359 Simplifying t + -0.5102040815 = -2.179473359 Reorder the terms: -0.5102040815 + t = -2.179473359 Solving -0.5102040815 + t = -2.179473359 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 = -2.179473359 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -2.179473359 + 0.5102040815 t = -2.179473359 + 0.5102040815 Combine like terms: -2.179473359 + 0.5102040815 = -1.6692692775 t = -1.6692692775 Simplifying t = -1.6692692775Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.6896774405, -1.6692692775}
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