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Simplifying 16t2 + -400t + -3 = 0 Reorder the terms: -3 + -400t + 16t2 = 0 Solving -3 + -400t + 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 + -25t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -25t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -25t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -25t + t2 = 0 + 0.1875 -25t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -25t + t2 = 0.1875 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = 0.1875 + 156.25 Reorder the terms: 156.25 + -25t + t2 = 0.1875 + 156.25 Combine like terms: 0.1875 + 156.25 = 156.4375 156.25 + -25t + t2 = 156.4375 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 156.4375 Calculate the square root of the right side: 12.507497751 Break this problem into two subproblems by setting (t + -12.5) equal to 12.507497751 and -12.507497751.Subproblem 1
t + -12.5 = 12.507497751 Simplifying t + -12.5 = 12.507497751 Reorder the terms: -12.5 + t = 12.507497751 Solving -12.5 + t = 12.507497751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 12.507497751 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 12.507497751 + 12.5 t = 12.507497751 + 12.5 Combine like terms: 12.507497751 + 12.5 = 25.007497751 t = 25.007497751 Simplifying t = 25.007497751Subproblem 2
t + -12.5 = -12.507497751 Simplifying t + -12.5 = -12.507497751 Reorder the terms: -12.5 + t = -12.507497751 Solving -12.5 + t = -12.507497751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -12.507497751 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -12.507497751 + 12.5 t = -12.507497751 + 12.5 Combine like terms: -12.507497751 + 12.5 = -0.007497751 t = -0.007497751 Simplifying t = -0.007497751Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.007497751, -0.007497751}
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