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Simplifying 5t + -4.9t2 = -1.8 Solving 5t + -4.9t2 = -1.8 Solving for variable 't'. Reorder the terms: 1.8 + 5t + -4.9t2 = -1.8 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 1.8 + 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'. -0.3673469388 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '0.3673469388' to each side of the equation. -0.3673469388 + -1.020408163t + 0.3673469388 + t2 = 0 + 0.3673469388 Reorder the terms: -0.3673469388 + 0.3673469388 + -1.020408163t + t2 = 0 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + -1.020408163t + t2 = 0 + 0.3673469388 -1.020408163t + t2 = 0 + 0.3673469388 Combine like terms: 0 + 0.3673469388 = 0.3673469388 -1.020408163t + t2 = 0.3673469388 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 = 0.3673469388 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 0.3673469388 + 0.2603082048 Combine like terms: 0.3673469388 + 0.2603082048 = 0.6276551436 0.2603082048 + -1.020408163t + t2 = 0.6276551436 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 0.6276551436 Calculate the square root of the right side: 0.792246896 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 0.792246896 and -0.792246896.Subproblem 1
t + -0.5102040815 = 0.792246896 Simplifying t + -0.5102040815 = 0.792246896 Reorder the terms: -0.5102040815 + t = 0.792246896 Solving -0.5102040815 + t = 0.792246896 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 = 0.792246896 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 0.792246896 + 0.5102040815 t = 0.792246896 + 0.5102040815 Combine like terms: 0.792246896 + 0.5102040815 = 1.3024509775 t = 1.3024509775 Simplifying t = 1.3024509775Subproblem 2
t + -0.5102040815 = -0.792246896 Simplifying t + -0.5102040815 = -0.792246896 Reorder the terms: -0.5102040815 + t = -0.792246896 Solving -0.5102040815 + t = -0.792246896 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 = -0.792246896 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -0.792246896 + 0.5102040815 t = -0.792246896 + 0.5102040815 Combine like terms: -0.792246896 + 0.5102040815 = -0.2820428145 t = -0.2820428145 Simplifying t = -0.2820428145Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3024509775, -0.2820428145}
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