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Simplifying 16t2 + -105t + 34 = 0 Reorder the terms: 34 + -105t + 16t2 = 0 Solving 34 + -105t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.125 + -6.5625t + t2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -6.5625t + -2.125 + t2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -6.5625t + t2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -6.5625t + t2 = 0 + -2.125 -6.5625t + t2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -6.5625t + t2 = -2.125 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 = -2.125 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = -2.125 + 10.76660156 Combine like terms: -2.125 + 10.76660156 = 8.64160156 10.76660156 + -6.5625t + t2 = 8.64160156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 8.64160156 Calculate the square root of the right side: 2.93966011 Break this problem into two subproblems by setting (t + -3.28125) equal to 2.93966011 and -2.93966011.Subproblem 1
t + -3.28125 = 2.93966011 Simplifying t + -3.28125 = 2.93966011 Reorder the terms: -3.28125 + t = 2.93966011 Solving -3.28125 + t = 2.93966011 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 = 2.93966011 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 2.93966011 + 3.28125 t = 2.93966011 + 3.28125 Combine like terms: 2.93966011 + 3.28125 = 6.22091011 t = 6.22091011 Simplifying t = 6.22091011Subproblem 2
t + -3.28125 = -2.93966011 Simplifying t + -3.28125 = -2.93966011 Reorder the terms: -3.28125 + t = -2.93966011 Solving -3.28125 + t = -2.93966011 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 = -2.93966011 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -2.93966011 + 3.28125 t = -2.93966011 + 3.28125 Combine like terms: -2.93966011 + 3.28125 = 0.34158989 t = 0.34158989 Simplifying t = 0.34158989Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.22091011, 0.34158989}
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