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Simplifying 1.1 = 8.2t + -4.9t2 Solving 1.1 = 8.2t + -4.9t2 Solving for variable 't'. Reorder the terms: 1.1 + -8.2t + 4.9t2 = 8.2t + -8.2t + -4.9t2 + 4.9t2 Combine like terms: 8.2t + -8.2t = 0.0 1.1 + -8.2t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 1.1 + -8.2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 1.1 + -8.2t + 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'. 0.2244897959 + -1.673469388t + t2 = 0 Move the constant term to the right: Add '-0.2244897959' to each side of the equation. 0.2244897959 + -1.673469388t + -0.2244897959 + t2 = 0 + -0.2244897959 Reorder the terms: 0.2244897959 + -0.2244897959 + -1.673469388t + t2 = 0 + -0.2244897959 Combine like terms: 0.2244897959 + -0.2244897959 = 0.0000000000 0.0000000000 + -1.673469388t + t2 = 0 + -0.2244897959 -1.673469388t + t2 = 0 + -0.2244897959 Combine like terms: 0 + -0.2244897959 = -0.2244897959 -1.673469388t + t2 = -0.2244897959 The t term is -1.673469388t. Take half its coefficient (-0.836734694). Square it (0.7001249481) and add it to both sides. Add '0.7001249481' to each side of the equation. -1.673469388t + 0.7001249481 + t2 = -0.2244897959 + 0.7001249481 Reorder the terms: 0.7001249481 + -1.673469388t + t2 = -0.2244897959 + 0.7001249481 Combine like terms: -0.2244897959 + 0.7001249481 = 0.4756351522 0.7001249481 + -1.673469388t + t2 = 0.4756351522 Factor a perfect square on the left side: (t + -0.836734694)(t + -0.836734694) = 0.4756351522 Calculate the square root of the right side: 0.689663072 Break this problem into two subproblems by setting (t + -0.836734694) equal to 0.689663072 and -0.689663072.Subproblem 1
t + -0.836734694 = 0.689663072 Simplifying t + -0.836734694 = 0.689663072 Reorder the terms: -0.836734694 + t = 0.689663072 Solving -0.836734694 + t = 0.689663072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.836734694' to each side of the equation. -0.836734694 + 0.836734694 + t = 0.689663072 + 0.836734694 Combine like terms: -0.836734694 + 0.836734694 = 0.000000000 0.000000000 + t = 0.689663072 + 0.836734694 t = 0.689663072 + 0.836734694 Combine like terms: 0.689663072 + 0.836734694 = 1.526397766 t = 1.526397766 Simplifying t = 1.526397766Subproblem 2
t + -0.836734694 = -0.689663072 Simplifying t + -0.836734694 = -0.689663072 Reorder the terms: -0.836734694 + t = -0.689663072 Solving -0.836734694 + t = -0.689663072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.836734694' to each side of the equation. -0.836734694 + 0.836734694 + t = -0.689663072 + 0.836734694 Combine like terms: -0.836734694 + 0.836734694 = 0.000000000 0.000000000 + t = -0.689663072 + 0.836734694 t = -0.689663072 + 0.836734694 Combine like terms: -0.689663072 + 0.836734694 = 0.147071622 t = 0.147071622 Simplifying t = 0.147071622Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.526397766, 0.147071622}
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