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Simplifying 4.9t2 + -18t + 8 = 0 Reorder the terms: 8 + -18t + 4.9t2 = 0 Solving 8 + -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'. 1.632653061 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '-1.632653061' to each side of the equation. 1.632653061 + -3.673469388t + -1.632653061 + t2 = 0 + -1.632653061 Reorder the terms: 1.632653061 + -1.632653061 + -3.673469388t + t2 = 0 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + -3.673469388t + t2 = 0 + -1.632653061 -3.673469388t + t2 = 0 + -1.632653061 Combine like terms: 0 + -1.632653061 = -1.632653061 -3.673469388t + t2 = -1.632653061 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 = -1.632653061 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = -1.632653061 + 3.373594336 Combine like terms: -1.632653061 + 3.373594336 = 1.740941275 3.373594336 + -3.673469388t + t2 = 1.740941275 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 1.740941275 Calculate the square root of the right side: 1.319447337 Break this problem into two subproblems by setting (t + -1.836734694) equal to 1.319447337 and -1.319447337.Subproblem 1
t + -1.836734694 = 1.319447337 Simplifying t + -1.836734694 = 1.319447337 Reorder the terms: -1.836734694 + t = 1.319447337 Solving -1.836734694 + t = 1.319447337 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 = 1.319447337 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 1.319447337 + 1.836734694 t = 1.319447337 + 1.836734694 Combine like terms: 1.319447337 + 1.836734694 = 3.156182031 t = 3.156182031 Simplifying t = 3.156182031Subproblem 2
t + -1.836734694 = -1.319447337 Simplifying t + -1.836734694 = -1.319447337 Reorder the terms: -1.836734694 + t = -1.319447337 Solving -1.836734694 + t = -1.319447337 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 = -1.319447337 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -1.319447337 + 1.836734694 t = -1.319447337 + 1.836734694 Combine like terms: -1.319447337 + 1.836734694 = 0.517287357 t = 0.517287357 Simplifying t = 0.517287357Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.156182031, 0.517287357}
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