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Simplifying -4.9t2 + 3805t + 5.6 = 0 Reorder the terms: 5.6 + 3805t + -4.9t2 = 0 Solving 5.6 + 3805t + -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'. -1.142857143 + -776.5306122t + t2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -776.5306122t + 1.142857143 + t2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -776.5306122t + t2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -776.5306122t + t2 = 0 + 1.142857143 -776.5306122t + t2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -776.5306122t + t2 = 1.142857143 The t term is -776.5306122t. Take half its coefficient (-388.2653061). Square it (150749.9479) and add it to both sides. Add '150749.9479' to each side of the equation. -776.5306122t + 150749.9479 + t2 = 1.142857143 + 150749.9479 Reorder the terms: 150749.9479 + -776.5306122t + t2 = 1.142857143 + 150749.9479 Combine like terms: 1.142857143 + 150749.9479 = 150751.090757143 150749.9479 + -776.5306122t + t2 = 150751.090757143 Factor a perfect square on the left side: (t + -388.2653061)(t + -388.2653061) = 150751.090757143 Calculate the square root of the right side: 388.266777818 Break this problem into two subproblems by setting (t + -388.2653061) equal to 388.266777818 and -388.266777818.Subproblem 1
t + -388.2653061 = 388.266777818 Simplifying t + -388.2653061 = 388.266777818 Reorder the terms: -388.2653061 + t = 388.266777818 Solving -388.2653061 + t = 388.266777818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '388.2653061' to each side of the equation. -388.2653061 + 388.2653061 + t = 388.266777818 + 388.2653061 Combine like terms: -388.2653061 + 388.2653061 = 0.0000000 0.0000000 + t = 388.266777818 + 388.2653061 t = 388.266777818 + 388.2653061 Combine like terms: 388.266777818 + 388.2653061 = 776.532083918 t = 776.532083918 Simplifying t = 776.532083918Subproblem 2
t + -388.2653061 = -388.266777818 Simplifying t + -388.2653061 = -388.266777818 Reorder the terms: -388.2653061 + t = -388.266777818 Solving -388.2653061 + t = -388.266777818 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '388.2653061' to each side of the equation. -388.2653061 + 388.2653061 + t = -388.266777818 + 388.2653061 Combine like terms: -388.2653061 + 388.2653061 = 0.0000000 0.0000000 + t = -388.266777818 + 388.2653061 t = -388.266777818 + 388.2653061 Combine like terms: -388.266777818 + 388.2653061 = -0.001471718 t = -0.001471718 Simplifying t = -0.001471718Solution
The solution to the problem is based on the solutions from the subproblems. t = {776.532083918, -0.001471718}
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