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Simplifying 1 = -4.9t2 + -5t + 2 Reorder the terms: 1 = 2 + -5t + -4.9t2 Solving 1 = 2 + -5t + -4.9t2 Solving for variable 't'. Combine like terms: 1 + -2 = -1 -1 + 5t + 4.9t2 = 2 + -5t + -4.9t2 + -2 + 5t + 4.9t2 Reorder the terms: -1 + 5t + 4.9t2 = 2 + -2 + -5t + 5t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -1 + 5t + 4.9t2 = 0 + -5t + 5t + -4.9t2 + 4.9t2 -1 + 5t + 4.9t2 = -5t + 5t + -4.9t2 + 4.9t2 Combine like terms: -5t + 5t = 0 -1 + 5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -1 + 5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1 + 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'. -0.2040816327 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + 1.020408163t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + 1.020408163t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + 1.020408163t + t2 = 0 + 0.2040816327 1.020408163t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 1.020408163t + t2 = 0.2040816327 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 = 0.2040816327 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 0.2040816327 + 0.2603082048 Combine like terms: 0.2040816327 + 0.2603082048 = 0.4643898375 0.2603082048 + 1.020408163t + t2 = 0.4643898375 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 0.4643898375 Calculate the square root of the right side: 0.681461545 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 0.681461545 and -0.681461545.Subproblem 1
t + 0.5102040815 = 0.681461545 Simplifying t + 0.5102040815 = 0.681461545 Reorder the terms: 0.5102040815 + t = 0.681461545 Solving 0.5102040815 + t = 0.681461545 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 = 0.681461545 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 0.681461545 + -0.5102040815 t = 0.681461545 + -0.5102040815 Combine like terms: 0.681461545 + -0.5102040815 = 0.1712574635 t = 0.1712574635 Simplifying t = 0.1712574635Subproblem 2
t + 0.5102040815 = -0.681461545 Simplifying t + 0.5102040815 = -0.681461545 Reorder the terms: 0.5102040815 + t = -0.681461545 Solving 0.5102040815 + t = -0.681461545 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 = -0.681461545 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -0.681461545 + -0.5102040815 t = -0.681461545 + -0.5102040815 Combine like terms: -0.681461545 + -0.5102040815 = -1.1916656265 t = -1.1916656265 Simplifying t = -1.1916656265Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.1712574635, -1.1916656265}
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