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Simplifying 4.9t2 + 360t + -2160 = 0 Reorder the terms: -2160 + 360t + 4.9t2 = 0 Solving -2160 + 360t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -440.8163265 + 73.46938776t + t2 = 0 Move the constant term to the right: Add '440.8163265' to each side of the equation. -440.8163265 + 73.46938776t + 440.8163265 + t2 = 0 + 440.8163265 Reorder the terms: -440.8163265 + 440.8163265 + 73.46938776t + t2 = 0 + 440.8163265 Combine like terms: -440.8163265 + 440.8163265 = 0.0000000 0.0000000 + 73.46938776t + t2 = 0 + 440.8163265 73.46938776t + t2 = 0 + 440.8163265 Combine like terms: 0 + 440.8163265 = 440.8163265 73.46938776t + t2 = 440.8163265 The t term is 73.46938776t. Take half its coefficient (36.73469388). Square it (1349.437734) and add it to both sides. Add '1349.437734' to each side of the equation. 73.46938776t + 1349.437734 + t2 = 440.8163265 + 1349.437734 Reorder the terms: 1349.437734 + 73.46938776t + t2 = 440.8163265 + 1349.437734 Combine like terms: 440.8163265 + 1349.437734 = 1790.2540605 1349.437734 + 73.46938776t + t2 = 1790.2540605 Factor a perfect square on the left side: (t + 36.73469388)(t + 36.73469388) = 1790.2540605 Calculate the square root of the right side: 42.31139398 Break this problem into two subproblems by setting (t + 36.73469388) equal to 42.31139398 and -42.31139398.Subproblem 1
t + 36.73469388 = 42.31139398 Simplifying t + 36.73469388 = 42.31139398 Reorder the terms: 36.73469388 + t = 42.31139398 Solving 36.73469388 + t = 42.31139398 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-36.73469388' to each side of the equation. 36.73469388 + -36.73469388 + t = 42.31139398 + -36.73469388 Combine like terms: 36.73469388 + -36.73469388 = 0.00000000 0.00000000 + t = 42.31139398 + -36.73469388 t = 42.31139398 + -36.73469388 Combine like terms: 42.31139398 + -36.73469388 = 5.5767001 t = 5.5767001 Simplifying t = 5.5767001Subproblem 2
t + 36.73469388 = -42.31139398 Simplifying t + 36.73469388 = -42.31139398 Reorder the terms: 36.73469388 + t = -42.31139398 Solving 36.73469388 + t = -42.31139398 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-36.73469388' to each side of the equation. 36.73469388 + -36.73469388 + t = -42.31139398 + -36.73469388 Combine like terms: 36.73469388 + -36.73469388 = 0.00000000 0.00000000 + t = -42.31139398 + -36.73469388 t = -42.31139398 + -36.73469388 Combine like terms: -42.31139398 + -36.73469388 = -79.04608786 t = -79.04608786 Simplifying t = -79.04608786Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.5767001, -79.04608786}
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