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Simplifying 0 = -16t2 + 105t + 30 Reorder the terms: 0 = 30 + 105t + -16t2 Solving 0 = 30 + 105t + -16t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + -105t + 16t2 = 30 + 105t + -16t2 + -30 + -105t + 16t2 Reorder the terms: -30 + -105t + 16t2 = 30 + -30 + 105t + -105t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 -30 + -105t + 16t2 = 0 + 105t + -105t + -16t2 + 16t2 -30 + -105t + 16t2 = 105t + -105t + -16t2 + 16t2 Combine like terms: 105t + -105t = 0 -30 + -105t + 16t2 = 0 + -16t2 + 16t2 -30 + -105t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -105t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.875 + -6.5625t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -6.5625t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -6.5625t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -6.5625t + t2 = 0 + 1.875 -6.5625t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -6.5625t + t2 = 1.875 The t term is -6.5625t. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625t + 10.76660156 + t2 = 1.875 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = 1.875 + 10.76660156 Combine like terms: 1.875 + 10.76660156 = 12.64160156 10.76660156 + -6.5625t + t2 = 12.64160156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 12.64160156 Calculate the square root of the right side: 3.555502997 Break this problem into two subproblems by setting (t + -3.28125) equal to 3.555502997 and -3.555502997.Subproblem 1
t + -3.28125 = 3.555502997 Simplifying t + -3.28125 = 3.555502997 Reorder the terms: -3.28125 + t = 3.555502997 Solving -3.28125 + t = 3.555502997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = 3.555502997 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 3.555502997 + 3.28125 t = 3.555502997 + 3.28125 Combine like terms: 3.555502997 + 3.28125 = 6.836752997 t = 6.836752997 Simplifying t = 6.836752997Subproblem 2
t + -3.28125 = -3.555502997 Simplifying t + -3.28125 = -3.555502997 Reorder the terms: -3.28125 + t = -3.555502997 Solving -3.28125 + t = -3.555502997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = -3.555502997 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -3.555502997 + 3.28125 t = -3.555502997 + 3.28125 Combine like terms: -3.555502997 + 3.28125 = -0.274252997 t = -0.274252997 Simplifying t = -0.274252997Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.836752997, -0.274252997}
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