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Simplifying -4.9t2 + 56t + -40 = 0 Reorder the terms: -40 + 56t + -4.9t2 = 0 Solving -40 + 56t + -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'. 8.163265306 + -11.42857143t + t2 = 0 Move the constant term to the right: Add '-8.163265306' to each side of the equation. 8.163265306 + -11.42857143t + -8.163265306 + t2 = 0 + -8.163265306 Reorder the terms: 8.163265306 + -8.163265306 + -11.42857143t + t2 = 0 + -8.163265306 Combine like terms: 8.163265306 + -8.163265306 = 0.000000000 0.000000000 + -11.42857143t + t2 = 0 + -8.163265306 -11.42857143t + t2 = 0 + -8.163265306 Combine like terms: 0 + -8.163265306 = -8.163265306 -11.42857143t + t2 = -8.163265306 The t term is -11.42857143t. Take half its coefficient (-5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. -11.42857143t + 32.65306123 + t2 = -8.163265306 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143t + t2 = -8.163265306 + 32.65306123 Combine like terms: -8.163265306 + 32.65306123 = 24.489795924 32.65306123 + -11.42857143t + t2 = 24.489795924 Factor a perfect square on the left side: (t + -5.714285715)(t + -5.714285715) = 24.489795924 Calculate the square root of the right side: 4.948716594 Break this problem into two subproblems by setting (t + -5.714285715) equal to 4.948716594 and -4.948716594.Subproblem 1
t + -5.714285715 = 4.948716594 Simplifying t + -5.714285715 = 4.948716594 Reorder the terms: -5.714285715 + t = 4.948716594 Solving -5.714285715 + t = 4.948716594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + t = 4.948716594 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + t = 4.948716594 + 5.714285715 t = 4.948716594 + 5.714285715 Combine like terms: 4.948716594 + 5.714285715 = 10.663002309 t = 10.663002309 Simplifying t = 10.663002309Subproblem 2
t + -5.714285715 = -4.948716594 Simplifying t + -5.714285715 = -4.948716594 Reorder the terms: -5.714285715 + t = -4.948716594 Solving -5.714285715 + t = -4.948716594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + t = -4.948716594 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + t = -4.948716594 + 5.714285715 t = -4.948716594 + 5.714285715 Combine like terms: -4.948716594 + 5.714285715 = 0.765569121 t = 0.765569121 Simplifying t = 0.765569121Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.663002309, 0.765569121}
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