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Simplifying 4.9t2 + -18t + 15 = 0 Reorder the terms: 15 + -18t + 4.9t2 = 0 Solving 15 + -18t + 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'. 3.06122449 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -3.673469388t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -3.673469388t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -3.673469388t + t2 = 0 + -3.06122449 -3.673469388t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -3.673469388t + t2 = -3.06122449 The t term is -3.673469388t. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388t + 3.373594336 + t2 = -3.06122449 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = -3.06122449 + 3.373594336 Combine like terms: -3.06122449 + 3.373594336 = 0.312369846 3.373594336 + -3.673469388t + t2 = 0.312369846 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 0.312369846 Calculate the square root of the right side: 0.558900569 Break this problem into two subproblems by setting (t + -1.836734694) equal to 0.558900569 and -0.558900569.Subproblem 1
t + -1.836734694 = 0.558900569 Simplifying t + -1.836734694 = 0.558900569 Reorder the terms: -1.836734694 + t = 0.558900569 Solving -1.836734694 + t = 0.558900569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = 0.558900569 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 0.558900569 + 1.836734694 t = 0.558900569 + 1.836734694 Combine like terms: 0.558900569 + 1.836734694 = 2.395635263 t = 2.395635263 Simplifying t = 2.395635263Subproblem 2
t + -1.836734694 = -0.558900569 Simplifying t + -1.836734694 = -0.558900569 Reorder the terms: -1.836734694 + t = -0.558900569 Solving -1.836734694 + t = -0.558900569 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = -0.558900569 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -0.558900569 + 1.836734694 t = -0.558900569 + 1.836734694 Combine like terms: -0.558900569 + 1.836734694 = 1.277834125 t = 1.277834125 Simplifying t = 1.277834125Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.395635263, 1.277834125}
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