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Simplifying -0.017811t2 + 0.3812t + -1.085 = 0 Reorder the terms: -1.085 + 0.3812t + -0.017811t2 = 0 Solving -1.085 + 0.3812t + -0.017811t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.017811 the coefficient of the squared term: Divide each side by '-0.017811'. 60.91741059 + -21.40250407t + t2 = 0 Move the constant term to the right: Add '-60.91741059' to each side of the equation. 60.91741059 + -21.40250407t + -60.91741059 + t2 = 0 + -60.91741059 Reorder the terms: 60.91741059 + -60.91741059 + -21.40250407t + t2 = 0 + -60.91741059 Combine like terms: 60.91741059 + -60.91741059 = 0.00000000 0.00000000 + -21.40250407t + t2 = 0 + -60.91741059 -21.40250407t + t2 = 0 + -60.91741059 Combine like terms: 0 + -60.91741059 = -60.91741059 -21.40250407t + t2 = -60.91741059 The t term is -21.40250407t. Take half its coefficient (-10.70125204). Square it (114.5167952) and add it to both sides. Add '114.5167952' to each side of the equation. -21.40250407t + 114.5167952 + t2 = -60.91741059 + 114.5167952 Reorder the terms: 114.5167952 + -21.40250407t + t2 = -60.91741059 + 114.5167952 Combine like terms: -60.91741059 + 114.5167952 = 53.59938461 114.5167952 + -21.40250407t + t2 = 53.59938461 Factor a perfect square on the left side: (t + -10.70125204)(t + -10.70125204) = 53.59938461 Calculate the square root of the right side: 7.321160059 Break this problem into two subproblems by setting (t + -10.70125204) equal to 7.321160059 and -7.321160059.Subproblem 1
t + -10.70125204 = 7.321160059 Simplifying t + -10.70125204 = 7.321160059 Reorder the terms: -10.70125204 + t = 7.321160059 Solving -10.70125204 + t = 7.321160059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.70125204' to each side of the equation. -10.70125204 + 10.70125204 + t = 7.321160059 + 10.70125204 Combine like terms: -10.70125204 + 10.70125204 = 0.00000000 0.00000000 + t = 7.321160059 + 10.70125204 t = 7.321160059 + 10.70125204 Combine like terms: 7.321160059 + 10.70125204 = 18.022412099 t = 18.022412099 Simplifying t = 18.022412099Subproblem 2
t + -10.70125204 = -7.321160059 Simplifying t + -10.70125204 = -7.321160059 Reorder the terms: -10.70125204 + t = -7.321160059 Solving -10.70125204 + t = -7.321160059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.70125204' to each side of the equation. -10.70125204 + 10.70125204 + t = -7.321160059 + 10.70125204 Combine like terms: -10.70125204 + 10.70125204 = 0.00000000 0.00000000 + t = -7.321160059 + 10.70125204 t = -7.321160059 + 10.70125204 Combine like terms: -7.321160059 + 10.70125204 = 3.380091981 t = 3.380091981 Simplifying t = 3.380091981Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.022412099, 3.380091981}
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