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Simplifying 5.75 = -16t2 + 184t + 20 Reorder the terms: 5.75 = 20 + 184t + -16t2 Solving 5.75 = 20 + 184t + -16t2 Solving for variable 't'. Combine like terms: 5.75 + -20 = -14.25 -14.25 + -184t + 16t2 = 20 + 184t + -16t2 + -20 + -184t + 16t2 Reorder the terms: -14.25 + -184t + 16t2 = 20 + -20 + 184t + -184t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -14.25 + -184t + 16t2 = 0 + 184t + -184t + -16t2 + 16t2 -14.25 + -184t + 16t2 = 184t + -184t + -16t2 + 16t2 Combine like terms: 184t + -184t = 0 -14.25 + -184t + 16t2 = 0 + -16t2 + 16t2 -14.25 + -184t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -14.25 + -184t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.890625 + -11.5t + t2 = 0 Move the constant term to the right: Add '0.890625' to each side of the equation. -0.890625 + -11.5t + 0.890625 + t2 = 0 + 0.890625 Reorder the terms: -0.890625 + 0.890625 + -11.5t + t2 = 0 + 0.890625 Combine like terms: -0.890625 + 0.890625 = 0.000000 0.000000 + -11.5t + t2 = 0 + 0.890625 -11.5t + t2 = 0 + 0.890625 Combine like terms: 0 + 0.890625 = 0.890625 -11.5t + t2 = 0.890625 The t term is -11.5t. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5t + 33.0625 + t2 = 0.890625 + 33.0625 Reorder the terms: 33.0625 + -11.5t + t2 = 0.890625 + 33.0625 Combine like terms: 0.890625 + 33.0625 = 33.953125 33.0625 + -11.5t + t2 = 33.953125 Factor a perfect square on the left side: (t + -5.75)(t + -5.75) = 33.953125 Calculate the square root of the right side: 5.82693101 Break this problem into two subproblems by setting (t + -5.75) equal to 5.82693101 and -5.82693101.Subproblem 1
t + -5.75 = 5.82693101 Simplifying t + -5.75 = 5.82693101 Reorder the terms: -5.75 + t = 5.82693101 Solving -5.75 + t = 5.82693101 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + t = 5.82693101 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + t = 5.82693101 + 5.75 t = 5.82693101 + 5.75 Combine like terms: 5.82693101 + 5.75 = 11.57693101 t = 11.57693101 Simplifying t = 11.57693101Subproblem 2
t + -5.75 = -5.82693101 Simplifying t + -5.75 = -5.82693101 Reorder the terms: -5.75 + t = -5.82693101 Solving -5.75 + t = -5.82693101 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + t = -5.82693101 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + t = -5.82693101 + 5.75 t = -5.82693101 + 5.75 Combine like terms: -5.82693101 + 5.75 = -0.07693101 t = -0.07693101 Simplifying t = -0.07693101Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.57693101, -0.07693101}
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