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Simplifying 0 = -16t2 + 73t + 6 Reorder the terms: 0 = 6 + 73t + -16t2 Solving 0 = 6 + 73t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -73t + 16t2 = 6 + 73t + -16t2 + -6 + -73t + 16t2 Reorder the terms: -6 + -73t + 16t2 = 6 + -6 + 73t + -73t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -73t + 16t2 = 0 + 73t + -73t + -16t2 + 16t2 -6 + -73t + 16t2 = 73t + -73t + -16t2 + 16t2 Combine like terms: 73t + -73t = 0 -6 + -73t + 16t2 = 0 + -16t2 + 16t2 -6 + -73t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -73t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -4.5625t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -4.5625t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -4.5625t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -4.5625t + t2 = 0 + 0.375 -4.5625t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -4.5625t + t2 = 0.375 The t term is -4.5625t. Take half its coefficient (-2.28125). Square it (5.204101563) and add it to both sides. Add '5.204101563' to each side of the equation. -4.5625t + 5.204101563 + t2 = 0.375 + 5.204101563 Reorder the terms: 5.204101563 + -4.5625t + t2 = 0.375 + 5.204101563 Combine like terms: 0.375 + 5.204101563 = 5.579101563 5.204101563 + -4.5625t + t2 = 5.579101563 Factor a perfect square on the left side: (t + -2.28125)(t + -2.28125) = 5.579101563 Calculate the square root of the right side: 2.362012185 Break this problem into two subproblems by setting (t + -2.28125) equal to 2.362012185 and -2.362012185.Subproblem 1
t + -2.28125 = 2.362012185 Simplifying t + -2.28125 = 2.362012185 Reorder the terms: -2.28125 + t = 2.362012185 Solving -2.28125 + t = 2.362012185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.28125' to each side of the equation. -2.28125 + 2.28125 + t = 2.362012185 + 2.28125 Combine like terms: -2.28125 + 2.28125 = 0.00000 0.00000 + t = 2.362012185 + 2.28125 t = 2.362012185 + 2.28125 Combine like terms: 2.362012185 + 2.28125 = 4.643262185 t = 4.643262185 Simplifying t = 4.643262185Subproblem 2
t + -2.28125 = -2.362012185 Simplifying t + -2.28125 = -2.362012185 Reorder the terms: -2.28125 + t = -2.362012185 Solving -2.28125 + t = -2.362012185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.28125' to each side of the equation. -2.28125 + 2.28125 + t = -2.362012185 + 2.28125 Combine like terms: -2.28125 + 2.28125 = 0.00000 0.00000 + t = -2.362012185 + 2.28125 t = -2.362012185 + 2.28125 Combine like terms: -2.362012185 + 2.28125 = -0.080762185 t = -0.080762185 Simplifying t = -0.080762185Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.643262185, -0.080762185}
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