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Simplifying 0.33t2 + 96t + -800 = 0 Reorder the terms: -800 + 96t + 0.33t2 = 0 Solving -800 + 96t + 0.33t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -2424.242424 + 290.9090909t + t2 = 0 Move the constant term to the right: Add '2424.242424' to each side of the equation. -2424.242424 + 290.9090909t + 2424.242424 + t2 = 0 + 2424.242424 Reorder the terms: -2424.242424 + 2424.242424 + 290.9090909t + t2 = 0 + 2424.242424 Combine like terms: -2424.242424 + 2424.242424 = 0.000000 0.000000 + 290.9090909t + t2 = 0 + 2424.242424 290.9090909t + t2 = 0 + 2424.242424 Combine like terms: 0 + 2424.242424 = 2424.242424 290.9090909t + t2 = 2424.242424 The t term is 290.9090909t. Take half its coefficient (145.4545455). Square it (21157.02481) and add it to both sides. Add '21157.02481' to each side of the equation. 290.9090909t + 21157.02481 + t2 = 2424.242424 + 21157.02481 Reorder the terms: 21157.02481 + 290.9090909t + t2 = 2424.242424 + 21157.02481 Combine like terms: 2424.242424 + 21157.02481 = 23581.267234 21157.02481 + 290.9090909t + t2 = 23581.267234 Factor a perfect square on the left side: (t + 145.4545455)(t + 145.4545455) = 23581.267234 Calculate the square root of the right side: 153.561932894 Break this problem into two subproblems by setting (t + 145.4545455) equal to 153.561932894 and -153.561932894.Subproblem 1
t + 145.4545455 = 153.561932894 Simplifying t + 145.4545455 = 153.561932894 Reorder the terms: 145.4545455 + t = 153.561932894 Solving 145.4545455 + t = 153.561932894 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-145.4545455' to each side of the equation. 145.4545455 + -145.4545455 + t = 153.561932894 + -145.4545455 Combine like terms: 145.4545455 + -145.4545455 = 0.0000000 0.0000000 + t = 153.561932894 + -145.4545455 t = 153.561932894 + -145.4545455 Combine like terms: 153.561932894 + -145.4545455 = 8.107387394 t = 8.107387394 Simplifying t = 8.107387394Subproblem 2
t + 145.4545455 = -153.561932894 Simplifying t + 145.4545455 = -153.561932894 Reorder the terms: 145.4545455 + t = -153.561932894 Solving 145.4545455 + t = -153.561932894 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-145.4545455' to each side of the equation. 145.4545455 + -145.4545455 + t = -153.561932894 + -145.4545455 Combine like terms: 145.4545455 + -145.4545455 = 0.0000000 0.0000000 + t = -153.561932894 + -145.4545455 t = -153.561932894 + -145.4545455 Combine like terms: -153.561932894 + -145.4545455 = -299.016478394 t = -299.016478394 Simplifying t = -299.016478394Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.107387394, -299.016478394}
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