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Simplifying 0 = -16t2 + 105t + 14 Reorder the terms: 0 = 14 + 105t + -16t2 Solving 0 = 14 + 105t + -16t2 Solving for variable 't'. Combine like terms: 0 + -14 = -14 -14 + -105t + 16t2 = 14 + 105t + -16t2 + -14 + -105t + 16t2 Reorder the terms: -14 + -105t + 16t2 = 14 + -14 + 105t + -105t + -16t2 + 16t2 Combine like terms: 14 + -14 = 0 -14 + -105t + 16t2 = 0 + 105t + -105t + -16t2 + 16t2 -14 + -105t + 16t2 = 105t + -105t + -16t2 + 16t2 Combine like terms: 105t + -105t = 0 -14 + -105t + 16t2 = 0 + -16t2 + 16t2 -14 + -105t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -14 + -105t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.875 + -6.5625t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -6.5625t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -6.5625t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -6.5625t + t2 = 0 + 0.875 -6.5625t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -6.5625t + t2 = 0.875 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 = 0.875 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = 0.875 + 10.76660156 Combine like terms: 0.875 + 10.76660156 = 11.64160156 10.76660156 + -6.5625t + t2 = 11.64160156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 11.64160156 Calculate the square root of the right side: 3.411979127 Break this problem into two subproblems by setting (t + -3.28125) equal to 3.411979127 and -3.411979127.Subproblem 1
t + -3.28125 = 3.411979127 Simplifying t + -3.28125 = 3.411979127 Reorder the terms: -3.28125 + t = 3.411979127 Solving -3.28125 + t = 3.411979127 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 = 3.411979127 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 3.411979127 + 3.28125 t = 3.411979127 + 3.28125 Combine like terms: 3.411979127 + 3.28125 = 6.693229127 t = 6.693229127 Simplifying t = 6.693229127Subproblem 2
t + -3.28125 = -3.411979127 Simplifying t + -3.28125 = -3.411979127 Reorder the terms: -3.28125 + t = -3.411979127 Solving -3.28125 + t = -3.411979127 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 = -3.411979127 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -3.411979127 + 3.28125 t = -3.411979127 + 3.28125 Combine like terms: -3.411979127 + 3.28125 = -0.130729127 t = -0.130729127 Simplifying t = -0.130729127Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.693229127, -0.130729127}
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