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Simplifying 4.9t2 + -5t + -280 = 0 Reorder the terms: -280 + -5t + 4.9t2 = 0 Solving -280 + -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'. -57.14285714 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '57.14285714' to each side of the equation. -57.14285714 + -1.020408163t + 57.14285714 + t2 = 0 + 57.14285714 Reorder the terms: -57.14285714 + 57.14285714 + -1.020408163t + t2 = 0 + 57.14285714 Combine like terms: -57.14285714 + 57.14285714 = 0.00000000 0.00000000 + -1.020408163t + t2 = 0 + 57.14285714 -1.020408163t + t2 = 0 + 57.14285714 Combine like terms: 0 + 57.14285714 = 57.14285714 -1.020408163t + t2 = 57.14285714 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 = 57.14285714 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 57.14285714 + 0.2603082048 Combine like terms: 57.14285714 + 0.2603082048 = 57.4031653448 0.2603082048 + -1.020408163t + t2 = 57.4031653448 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 57.4031653448 Calculate the square root of the right side: 7.576487665 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 7.576487665 and -7.576487665.Subproblem 1
t + -0.5102040815 = 7.576487665 Simplifying t + -0.5102040815 = 7.576487665 Reorder the terms: -0.5102040815 + t = 7.576487665 Solving -0.5102040815 + t = 7.576487665 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 = 7.576487665 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 7.576487665 + 0.5102040815 t = 7.576487665 + 0.5102040815 Combine like terms: 7.576487665 + 0.5102040815 = 8.0866917465 t = 8.0866917465 Simplifying t = 8.0866917465Subproblem 2
t + -0.5102040815 = -7.576487665 Simplifying t + -0.5102040815 = -7.576487665 Reorder the terms: -0.5102040815 + t = -7.576487665 Solving -0.5102040815 + t = -7.576487665 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 = -7.576487665 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -7.576487665 + 0.5102040815 t = -7.576487665 + 0.5102040815 Combine like terms: -7.576487665 + 0.5102040815 = -7.0662835835 t = -7.0662835835 Simplifying t = -7.0662835835Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.0866917465, -7.0662835835}
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