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Simplifying 16t2 + 200t + 3 = 0 Reorder the terms: 3 + 200t + 16t2 = 0 Solving 3 + 200t + 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'. 0.1875 + 12.5t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + 12.5t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + 12.5t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + 12.5t + t2 = 0 + -0.1875 12.5t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 12.5t + t2 = -0.1875 The t term is 12.5t. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5t + 39.0625 + t2 = -0.1875 + 39.0625 Reorder the terms: 39.0625 + 12.5t + t2 = -0.1875 + 39.0625 Combine like terms: -0.1875 + 39.0625 = 38.875 39.0625 + 12.5t + t2 = 38.875 Factor a perfect square on the left side: (t + 6.25)(t + 6.25) = 38.875 Calculate the square root of the right side: 6.234981957 Break this problem into two subproblems by setting (t + 6.25) equal to 6.234981957 and -6.234981957.Subproblem 1
t + 6.25 = 6.234981957 Simplifying t + 6.25 = 6.234981957 Reorder the terms: 6.25 + t = 6.234981957 Solving 6.25 + t = 6.234981957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + t = 6.234981957 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = 6.234981957 + -6.25 t = 6.234981957 + -6.25 Combine like terms: 6.234981957 + -6.25 = -0.015018043 t = -0.015018043 Simplifying t = -0.015018043Subproblem 2
t + 6.25 = -6.234981957 Simplifying t + 6.25 = -6.234981957 Reorder the terms: 6.25 + t = -6.234981957 Solving 6.25 + t = -6.234981957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + t = -6.234981957 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = -6.234981957 + -6.25 t = -6.234981957 + -6.25 Combine like terms: -6.234981957 + -6.25 = -12.484981957 t = -12.484981957 Simplifying t = -12.484981957Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.015018043, -12.484981957}
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