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Simplifying 0 = -4.9t2 + 18t + -11 Reorder the terms: 0 = -11 + 18t + -4.9t2 Solving 0 = -11 + 18t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 11 = 11 11 + -18t + 4.9t2 = -11 + 18t + -4.9t2 + 11 + -18t + 4.9t2 Reorder the terms: 11 + -18t + 4.9t2 = -11 + 11 + 18t + -18t + -4.9t2 + 4.9t2 Combine like terms: -11 + 11 = 0 11 + -18t + 4.9t2 = 0 + 18t + -18t + -4.9t2 + 4.9t2 11 + -18t + 4.9t2 = 18t + -18t + -4.9t2 + 4.9t2 Combine like terms: 18t + -18t = 0 11 + -18t + 4.9t2 = 0 + -4.9t2 + 4.9t2 11 + -18t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 11 + -18t + 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'. 2.244897959 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '-2.244897959' to each side of the equation. 2.244897959 + -3.673469388t + -2.244897959 + t2 = 0 + -2.244897959 Reorder the terms: 2.244897959 + -2.244897959 + -3.673469388t + t2 = 0 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + -3.673469388t + t2 = 0 + -2.244897959 -3.673469388t + t2 = 0 + -2.244897959 Combine like terms: 0 + -2.244897959 = -2.244897959 -3.673469388t + t2 = -2.244897959 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 = -2.244897959 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = -2.244897959 + 3.373594336 Combine like terms: -2.244897959 + 3.373594336 = 1.128696377 3.373594336 + -3.673469388t + t2 = 1.128696377 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 1.128696377 Calculate the square root of the right side: 1.062401232 Break this problem into two subproblems by setting (t + -1.836734694) equal to 1.062401232 and -1.062401232.Subproblem 1
t + -1.836734694 = 1.062401232 Simplifying t + -1.836734694 = 1.062401232 Reorder the terms: -1.836734694 + t = 1.062401232 Solving -1.836734694 + t = 1.062401232 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 = 1.062401232 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 1.062401232 + 1.836734694 t = 1.062401232 + 1.836734694 Combine like terms: 1.062401232 + 1.836734694 = 2.899135926 t = 2.899135926 Simplifying t = 2.899135926Subproblem 2
t + -1.836734694 = -1.062401232 Simplifying t + -1.836734694 = -1.062401232 Reorder the terms: -1.836734694 + t = -1.062401232 Solving -1.836734694 + t = -1.062401232 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 = -1.062401232 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -1.062401232 + 1.836734694 t = -1.062401232 + 1.836734694 Combine like terms: -1.062401232 + 1.836734694 = 0.774333462 t = 0.774333462 Simplifying t = 0.774333462Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.899135926, 0.774333462}
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