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Simplifying 16t2 + -8t + -16.5 = 0 Reorder the terms: -16.5 + -8t + 16t2 = 0 Solving -16.5 + -8t + 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'. -1.03125 + -0.5t + t2 = 0 Move the constant term to the right: Add '1.03125' to each side of the equation. -1.03125 + -0.5t + 1.03125 + t2 = 0 + 1.03125 Reorder the terms: -1.03125 + 1.03125 + -0.5t + t2 = 0 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + -0.5t + t2 = 0 + 1.03125 -0.5t + t2 = 0 + 1.03125 Combine like terms: 0 + 1.03125 = 1.03125 -0.5t + t2 = 1.03125 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 1.03125 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 1.03125 + 0.0625 Combine like terms: 1.03125 + 0.0625 = 1.09375 0.0625 + -0.5t + t2 = 1.09375 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 1.09375 Calculate the square root of the right side: 1.045825033 Break this problem into two subproblems by setting (t + -0.25) equal to 1.045825033 and -1.045825033.Subproblem 1
t + -0.25 = 1.045825033 Simplifying t + -0.25 = 1.045825033 Reorder the terms: -0.25 + t = 1.045825033 Solving -0.25 + t = 1.045825033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.045825033 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.045825033 + 0.25 t = 1.045825033 + 0.25 Combine like terms: 1.045825033 + 0.25 = 1.295825033 t = 1.295825033 Simplifying t = 1.295825033Subproblem 2
t + -0.25 = -1.045825033 Simplifying t + -0.25 = -1.045825033 Reorder the terms: -0.25 + t = -1.045825033 Solving -0.25 + t = -1.045825033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.045825033 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.045825033 + 0.25 t = -1.045825033 + 0.25 Combine like terms: -1.045825033 + 0.25 = -0.795825033 t = -0.795825033 Simplifying t = -0.795825033Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.295825033, -0.795825033}
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