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Simplifying 0 = -16t2 + 175t + -85 Reorder the terms: 0 = -85 + 175t + -16t2 Solving 0 = -85 + 175t + -16t2 Solving for variable 't'. Combine like terms: 0 + 85 = 85 85 + -175t + 16t2 = -85 + 175t + -16t2 + 85 + -175t + 16t2 Reorder the terms: 85 + -175t + 16t2 = -85 + 85 + 175t + -175t + -16t2 + 16t2 Combine like terms: -85 + 85 = 0 85 + -175t + 16t2 = 0 + 175t + -175t + -16t2 + 16t2 85 + -175t + 16t2 = 175t + -175t + -16t2 + 16t2 Combine like terms: 175t + -175t = 0 85 + -175t + 16t2 = 0 + -16t2 + 16t2 85 + -175t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 85 + -175t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.3125 + -10.9375t + t2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + -10.9375t + -5.3125 + t2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + -10.9375t + t2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + -10.9375t + t2 = 0 + -5.3125 -10.9375t + t2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 -10.9375t + t2 = -5.3125 The t term is -10.9375t. Take half its coefficient (-5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. -10.9375t + 29.90722656 + t2 = -5.3125 + 29.90722656 Reorder the terms: 29.90722656 + -10.9375t + t2 = -5.3125 + 29.90722656 Combine like terms: -5.3125 + 29.90722656 = 24.59472656 29.90722656 + -10.9375t + t2 = 24.59472656 Factor a perfect square on the left side: (t + -5.46875)(t + -5.46875) = 24.59472656 Calculate the square root of the right side: 4.959307065 Break this problem into two subproblems by setting (t + -5.46875) equal to 4.959307065 and -4.959307065.Subproblem 1
t + -5.46875 = 4.959307065 Simplifying t + -5.46875 = 4.959307065 Reorder the terms: -5.46875 + t = 4.959307065 Solving -5.46875 + t = 4.959307065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = 4.959307065 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = 4.959307065 + 5.46875 t = 4.959307065 + 5.46875 Combine like terms: 4.959307065 + 5.46875 = 10.428057065 t = 10.428057065 Simplifying t = 10.428057065Subproblem 2
t + -5.46875 = -4.959307065 Simplifying t + -5.46875 = -4.959307065 Reorder the terms: -5.46875 + t = -4.959307065 Solving -5.46875 + t = -4.959307065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + t = -4.959307065 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + t = -4.959307065 + 5.46875 t = -4.959307065 + 5.46875 Combine like terms: -4.959307065 + 5.46875 = 0.509442935 t = 0.509442935 Simplifying t = 0.509442935Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.428057065, 0.509442935}
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