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Simplifying 13.37 = -4.9t2 + 35t Reorder the terms: 13.37 = 35t + -4.9t2 Solving 13.37 = 35t + -4.9t2 Solving for variable 't'. Reorder the terms: 13.37 + -35t + 4.9t2 = 35t + -35t + -4.9t2 + 4.9t2 Combine like terms: 35t + -35t = 0 13.37 + -35t + 4.9t2 = 0 + -4.9t2 + 4.9t2 13.37 + -35t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 13.37 + -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'. 2.728571429 + -7.142857143t + t2 = 0 Move the constant term to the right: Add '-2.728571429' to each side of the equation. 2.728571429 + -7.142857143t + -2.728571429 + t2 = 0 + -2.728571429 Reorder the terms: 2.728571429 + -2.728571429 + -7.142857143t + t2 = 0 + -2.728571429 Combine like terms: 2.728571429 + -2.728571429 = 0.000000000 0.000000000 + -7.142857143t + t2 = 0 + -2.728571429 -7.142857143t + t2 = 0 + -2.728571429 Combine like terms: 0 + -2.728571429 = -2.728571429 -7.142857143t + t2 = -2.728571429 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 = -2.728571429 + 12.75510204 Reorder the terms: 12.75510204 + -7.142857143t + t2 = -2.728571429 + 12.75510204 Combine like terms: -2.728571429 + 12.75510204 = 10.026530611 12.75510204 + -7.142857143t + t2 = 10.026530611 Factor a perfect square on the left side: (t + -3.571428572)(t + -3.571428572) = 10.026530611 Calculate the square root of the right side: 3.166469739 Break this problem into two subproblems by setting (t + -3.571428572) equal to 3.166469739 and -3.166469739.Subproblem 1
t + -3.571428572 = 3.166469739 Simplifying t + -3.571428572 = 3.166469739 Reorder the terms: -3.571428572 + t = 3.166469739 Solving -3.571428572 + t = 3.166469739 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 = 3.166469739 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = 3.166469739 + 3.571428572 t = 3.166469739 + 3.571428572 Combine like terms: 3.166469739 + 3.571428572 = 6.737898311 t = 6.737898311 Simplifying t = 6.737898311Subproblem 2
t + -3.571428572 = -3.166469739 Simplifying t + -3.571428572 = -3.166469739 Reorder the terms: -3.571428572 + t = -3.166469739 Solving -3.571428572 + t = -3.166469739 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 = -3.166469739 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = -3.166469739 + 3.571428572 t = -3.166469739 + 3.571428572 Combine like terms: -3.166469739 + 3.571428572 = 0.404958833 t = 0.404958833 Simplifying t = 0.404958833Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.737898311, 0.404958833}
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