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Simplifying 0.0795t2 + -0.886t + 1.725 = 0 Reorder the terms: 1.725 + -0.886t + 0.0795t2 = 0 Solving 1.725 + -0.886t + 0.0795t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 21.69811321 + -11.14465409t + t2 = 0 Move the constant term to the right: Add '-21.69811321' to each side of the equation. 21.69811321 + -11.14465409t + -21.69811321 + t2 = 0 + -21.69811321 Reorder the terms: 21.69811321 + -21.69811321 + -11.14465409t + t2 = 0 + -21.69811321 Combine like terms: 21.69811321 + -21.69811321 = 0.00000000 0.00000000 + -11.14465409t + t2 = 0 + -21.69811321 -11.14465409t + t2 = 0 + -21.69811321 Combine like terms: 0 + -21.69811321 = -21.69811321 -11.14465409t + t2 = -21.69811321 The t term is -11.14465409t. Take half its coefficient (-5.572327045). Square it (31.05082870) and add it to both sides. Add '31.05082870' to each side of the equation. -11.14465409t + 31.05082870 + t2 = -21.69811321 + 31.05082870 Reorder the terms: 31.05082870 + -11.14465409t + t2 = -21.69811321 + 31.05082870 Combine like terms: -21.69811321 + 31.05082870 = 9.35271549 31.05082870 + -11.14465409t + t2 = 9.35271549 Factor a perfect square on the left side: (t + -5.572327045)(t + -5.572327045) = 9.35271549 Calculate the square root of the right side: 3.058220968 Break this problem into two subproblems by setting (t + -5.572327045) equal to 3.058220968 and -3.058220968.Subproblem 1
t + -5.572327045 = 3.058220968 Simplifying t + -5.572327045 = 3.058220968 Reorder the terms: -5.572327045 + t = 3.058220968 Solving -5.572327045 + t = 3.058220968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.572327045' to each side of the equation. -5.572327045 + 5.572327045 + t = 3.058220968 + 5.572327045 Combine like terms: -5.572327045 + 5.572327045 = 0.000000000 0.000000000 + t = 3.058220968 + 5.572327045 t = 3.058220968 + 5.572327045 Combine like terms: 3.058220968 + 5.572327045 = 8.630548013 t = 8.630548013 Simplifying t = 8.630548013Subproblem 2
t + -5.572327045 = -3.058220968 Simplifying t + -5.572327045 = -3.058220968 Reorder the terms: -5.572327045 + t = -3.058220968 Solving -5.572327045 + t = -3.058220968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.572327045' to each side of the equation. -5.572327045 + 5.572327045 + t = -3.058220968 + 5.572327045 Combine like terms: -5.572327045 + 5.572327045 = 0.000000000 0.000000000 + t = -3.058220968 + 5.572327045 t = -3.058220968 + 5.572327045 Combine like terms: -3.058220968 + 5.572327045 = 2.514106077 t = 2.514106077 Simplifying t = 2.514106077Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.630548013, 2.514106077}
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