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Simplifying 354 = 35t + 0.5 * 9.8t2 Multiply 0.5 * 9.8 354 = 35t + 4.9t2 Solving 354 = 35t + 4.9t2 Solving for variable 't'. Reorder the terms: 354 + -35t + -4.9t2 = 35t + -35t + 4.9t2 + -4.9t2 Combine like terms: 35t + -35t = 0 354 + -35t + -4.9t2 = 0 + 4.9t2 + -4.9t2 354 + -35t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 354 + -35t + -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'. -72.24489796 + 7.142857143t + t2 = 0 Move the constant term to the right: Add '72.24489796' to each side of the equation. -72.24489796 + 7.142857143t + 72.24489796 + t2 = 0 + 72.24489796 Reorder the terms: -72.24489796 + 72.24489796 + 7.142857143t + t2 = 0 + 72.24489796 Combine like terms: -72.24489796 + 72.24489796 = 0.00000000 0.00000000 + 7.142857143t + t2 = 0 + 72.24489796 7.142857143t + t2 = 0 + 72.24489796 Combine like terms: 0 + 72.24489796 = 72.24489796 7.142857143t + t2 = 72.24489796 The t term is 7.142857143t. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143t + 12.75510204 + t2 = 72.24489796 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143t + t2 = 72.24489796 + 12.75510204 Combine like terms: 72.24489796 + 12.75510204 = 85 12.75510204 + 7.142857143t + t2 = 85 Factor a perfect square on the left side: (t + 3.571428572)(t + 3.571428572) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (t + 3.571428572) equal to 9.219544457 and -9.219544457.Subproblem 1
t + 3.571428572 = 9.219544457 Simplifying t + 3.571428572 = 9.219544457 Reorder the terms: 3.571428572 + t = 9.219544457 Solving 3.571428572 + t = 9.219544457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + t = 9.219544457 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + t = 9.219544457 + -3.571428572 t = 9.219544457 + -3.571428572 Combine like terms: 9.219544457 + -3.571428572 = 5.648115885 t = 5.648115885 Simplifying t = 5.648115885Subproblem 2
t + 3.571428572 = -9.219544457 Simplifying t + 3.571428572 = -9.219544457 Reorder the terms: 3.571428572 + t = -9.219544457 Solving 3.571428572 + t = -9.219544457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + t = -9.219544457 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + t = -9.219544457 + -3.571428572 t = -9.219544457 + -3.571428572 Combine like terms: -9.219544457 + -3.571428572 = -12.790973029 t = -12.790973029 Simplifying t = -12.790973029Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.648115885, -12.790973029}
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