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Simplifying 50 = -0.8t2 + 30t + 2 Reorder the terms: 50 = 2 + 30t + -0.8t2 Solving 50 = 2 + 30t + -0.8t2 Solving for variable 't'. Combine like terms: 50 + -2 = 48 48 + -30t + 0.8t2 = 2 + 30t + -0.8t2 + -2 + -30t + 0.8t2 Reorder the terms: 48 + -30t + 0.8t2 = 2 + -2 + 30t + -30t + -0.8t2 + 0.8t2 Combine like terms: 2 + -2 = 0 48 + -30t + 0.8t2 = 0 + 30t + -30t + -0.8t2 + 0.8t2 48 + -30t + 0.8t2 = 30t + -30t + -0.8t2 + 0.8t2 Combine like terms: 30t + -30t = 0 48 + -30t + 0.8t2 = 0 + -0.8t2 + 0.8t2 48 + -30t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 48 + -30t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 60 + -37.5t + t2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -37.5t + -60 + t2 = 0 + -60 Reorder the terms: 60 + -60 + -37.5t + t2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -37.5t + t2 = 0 + -60 -37.5t + t2 = 0 + -60 Combine like terms: 0 + -60 = -60 -37.5t + t2 = -60 The t term is -37.5t. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5t + 351.5625 + t2 = -60 + 351.5625 Reorder the terms: 351.5625 + -37.5t + t2 = -60 + 351.5625 Combine like terms: -60 + 351.5625 = 291.5625 351.5625 + -37.5t + t2 = 291.5625 Factor a perfect square on the left side: (t + -18.75)(t + -18.75) = 291.5625 Calculate the square root of the right side: 17.075201317 Break this problem into two subproblems by setting (t + -18.75) equal to 17.075201317 and -17.075201317.Subproblem 1
t + -18.75 = 17.075201317 Simplifying t + -18.75 = 17.075201317 Reorder the terms: -18.75 + t = 17.075201317 Solving -18.75 + t = 17.075201317 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + t = 17.075201317 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + t = 17.075201317 + 18.75 t = 17.075201317 + 18.75 Combine like terms: 17.075201317 + 18.75 = 35.825201317 t = 35.825201317 Simplifying t = 35.825201317Subproblem 2
t + -18.75 = -17.075201317 Simplifying t + -18.75 = -17.075201317 Reorder the terms: -18.75 + t = -17.075201317 Solving -18.75 + t = -17.075201317 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + t = -17.075201317 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + t = -17.075201317 + 18.75 t = -17.075201317 + 18.75 Combine like terms: -17.075201317 + 18.75 = 1.674798683 t = 1.674798683 Simplifying t = 1.674798683Solution
The solution to the problem is based on the solutions from the subproblems. t = {35.825201317, 1.674798683}
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