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Simplifying 29.4 = -0.002t2 + 0.5t Reorder the terms: 29.4 = 0.5t + -0.002t2 Solving 29.4 = 0.5t + -0.002t2 Solving for variable 't'. Reorder the terms: 29.4 + -0.5t + 0.002t2 = 0.5t + -0.5t + -0.002t2 + 0.002t2 Combine like terms: 0.5t + -0.5t = 0.0 29.4 + -0.5t + 0.002t2 = 0.0 + -0.002t2 + 0.002t2 29.4 + -0.5t + 0.002t2 = -0.002t2 + 0.002t2 Combine like terms: -0.002t2 + 0.002t2 = 0.000 29.4 + -0.5t + 0.002t2 = 0.000 Begin completing the square. Divide all terms by 0.002 the coefficient of the squared term: Divide each side by '0.002'. 14700 + -250t + t2 = 0 Move the constant term to the right: Add '-14700' to each side of the equation. 14700 + -250t + -14700 + t2 = 0 + -14700 Reorder the terms: 14700 + -14700 + -250t + t2 = 0 + -14700 Combine like terms: 14700 + -14700 = 0 0 + -250t + t2 = 0 + -14700 -250t + t2 = 0 + -14700 Combine like terms: 0 + -14700 = -14700 -250t + t2 = -14700 The t term is -250t. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250t + 15625 + t2 = -14700 + 15625 Reorder the terms: 15625 + -250t + t2 = -14700 + 15625 Combine like terms: -14700 + 15625 = 925 15625 + -250t + t2 = 925 Factor a perfect square on the left side: (t + -125)(t + -125) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (t + -125) equal to 30.413812651 and -30.413812651.Subproblem 1
t + -125 = 30.413812651 Simplifying t + -125 = 30.413812651 Reorder the terms: -125 + t = 30.413812651 Solving -125 + t = 30.413812651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + t = 30.413812651 + 125 Combine like terms: -125 + 125 = 0 0 + t = 30.413812651 + 125 t = 30.413812651 + 125 Combine like terms: 30.413812651 + 125 = 155.413812651 t = 155.413812651 Simplifying t = 155.413812651Subproblem 2
t + -125 = -30.413812651 Simplifying t + -125 = -30.413812651 Reorder the terms: -125 + t = -30.413812651 Solving -125 + t = -30.413812651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + t = -30.413812651 + 125 Combine like terms: -125 + 125 = 0 0 + t = -30.413812651 + 125 t = -30.413812651 + 125 Combine like terms: -30.413812651 + 125 = 94.586187349 t = 94.586187349 Simplifying t = 94.586187349Solution
The solution to the problem is based on the solutions from the subproblems. t = {155.413812651, 94.586187349}
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