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Simplifying 0 = -16t2 + 80t + 12389 Reorder the terms: 0 = 12389 + 80t + -16t2 Solving 0 = 12389 + 80t + -16t2 Solving for variable 't'. Combine like terms: 0 + -12389 = -12389 -12389 + -80t + 16t2 = 12389 + 80t + -16t2 + -12389 + -80t + 16t2 Reorder the terms: -12389 + -80t + 16t2 = 12389 + -12389 + 80t + -80t + -16t2 + 16t2 Combine like terms: 12389 + -12389 = 0 -12389 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 -12389 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 -12389 + -80t + 16t2 = 0 + -16t2 + 16t2 -12389 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12389 + -80t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -774.3125 + -5t + t2 = 0 Move the constant term to the right: Add '774.3125' to each side of the equation. -774.3125 + -5t + 774.3125 + t2 = 0 + 774.3125 Reorder the terms: -774.3125 + 774.3125 + -5t + t2 = 0 + 774.3125 Combine like terms: -774.3125 + 774.3125 = 0.0000 0.0000 + -5t + t2 = 0 + 774.3125 -5t + t2 = 0 + 774.3125 Combine like terms: 0 + 774.3125 = 774.3125 -5t + t2 = 774.3125 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 774.3125 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 774.3125 + 6.25 Combine like terms: 774.3125 + 6.25 = 780.5625 6.25 + -5t + t2 = 780.5625 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 780.5625 Calculate the square root of the right side: 27.938548638 Break this problem into two subproblems by setting (t + -2.5) equal to 27.938548638 and -27.938548638.Subproblem 1
t + -2.5 = 27.938548638 Simplifying t + -2.5 = 27.938548638 Reorder the terms: -2.5 + t = 27.938548638 Solving -2.5 + t = 27.938548638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 27.938548638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 27.938548638 + 2.5 t = 27.938548638 + 2.5 Combine like terms: 27.938548638 + 2.5 = 30.438548638 t = 30.438548638 Simplifying t = 30.438548638Subproblem 2
t + -2.5 = -27.938548638 Simplifying t + -2.5 = -27.938548638 Reorder the terms: -2.5 + t = -27.938548638 Solving -2.5 + t = -27.938548638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -27.938548638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -27.938548638 + 2.5 t = -27.938548638 + 2.5 Combine like terms: -27.938548638 + 2.5 = -25.438548638 t = -25.438548638 Simplifying t = -25.438548638Solution
The solution to the problem is based on the solutions from the subproblems. t = {30.438548638, -25.438548638}
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