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Simplifying 5.2 = -4.9t2 + 35t Reorder the terms: 5.2 = 35t + -4.9t2 Solving 5.2 = 35t + -4.9t2 Solving for variable 't'. Reorder the terms: 5.2 + -35t + 4.9t2 = 35t + -35t + -4.9t2 + 4.9t2 Combine like terms: 35t + -35t = 0 5.2 + -35t + 4.9t2 = 0 + -4.9t2 + 4.9t2 5.2 + -35t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 5.2 + -35t + 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'. 1.06122449 + -7.142857143t + t2 = 0 Move the constant term to the right: Add '-1.06122449' to each side of the equation. 1.06122449 + -7.142857143t + -1.06122449 + t2 = 0 + -1.06122449 Reorder the terms: 1.06122449 + -1.06122449 + -7.142857143t + t2 = 0 + -1.06122449 Combine like terms: 1.06122449 + -1.06122449 = 0.00000000 0.00000000 + -7.142857143t + t2 = 0 + -1.06122449 -7.142857143t + t2 = 0 + -1.06122449 Combine like terms: 0 + -1.06122449 = -1.06122449 -7.142857143t + t2 = -1.06122449 The t term is -7.142857143t. Take half its coefficient (-3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. -7.142857143t + 12.75510204 + t2 = -1.06122449 + 12.75510204 Reorder the terms: 12.75510204 + -7.142857143t + t2 = -1.06122449 + 12.75510204 Combine like terms: -1.06122449 + 12.75510204 = 11.69387755 12.75510204 + -7.142857143t + t2 = 11.69387755 Factor a perfect square on the left side: (t + -3.571428572)(t + -3.571428572) = 11.69387755 Calculate the square root of the right side: 3.419631201 Break this problem into two subproblems by setting (t + -3.571428572) equal to 3.419631201 and -3.419631201.Subproblem 1
t + -3.571428572 = 3.419631201 Simplifying t + -3.571428572 = 3.419631201 Reorder the terms: -3.571428572 + t = 3.419631201 Solving -3.571428572 + t = 3.419631201 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.571428572' to each side of the equation. -3.571428572 + 3.571428572 + t = 3.419631201 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = 3.419631201 + 3.571428572 t = 3.419631201 + 3.571428572 Combine like terms: 3.419631201 + 3.571428572 = 6.991059773 t = 6.991059773 Simplifying t = 6.991059773Subproblem 2
t + -3.571428572 = -3.419631201 Simplifying t + -3.571428572 = -3.419631201 Reorder the terms: -3.571428572 + t = -3.419631201 Solving -3.571428572 + t = -3.419631201 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.571428572' to each side of the equation. -3.571428572 + 3.571428572 + t = -3.419631201 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = -3.419631201 + 3.571428572 t = -3.419631201 + 3.571428572 Combine like terms: -3.419631201 + 3.571428572 = 0.151797371 t = 0.151797371 Simplifying t = 0.151797371Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.991059773, 0.151797371}
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