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Simplifying 200t + 16t2 = 625 Solving 200t + 16t2 = 625 Solving for variable 't'. Reorder the terms: -625 + 200t + 16t2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 200t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -39.0625 + 12.5t + t2 = 0 Move the constant term to the right: Add '39.0625' to each side of the equation. -39.0625 + 12.5t + 39.0625 + t2 = 0 + 39.0625 Reorder the terms: -39.0625 + 39.0625 + 12.5t + t2 = 0 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 0.0000 + 12.5t + t2 = 0 + 39.0625 12.5t + t2 = 0 + 39.0625 Combine like terms: 0 + 39.0625 = 39.0625 12.5t + t2 = 39.0625 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 = 39.0625 + 39.0625 Reorder the terms: 39.0625 + 12.5t + t2 = 39.0625 + 39.0625 Combine like terms: 39.0625 + 39.0625 = 78.125 39.0625 + 12.5t + t2 = 78.125 Factor a perfect square on the left side: (t + 6.25)(t + 6.25) = 78.125 Calculate the square root of the right side: 8.838834765 Break this problem into two subproblems by setting (t + 6.25) equal to 8.838834765 and -8.838834765.Subproblem 1
t + 6.25 = 8.838834765 Simplifying t + 6.25 = 8.838834765 Reorder the terms: 6.25 + t = 8.838834765 Solving 6.25 + t = 8.838834765 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 = 8.838834765 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = 8.838834765 + -6.25 t = 8.838834765 + -6.25 Combine like terms: 8.838834765 + -6.25 = 2.588834765 t = 2.588834765 Simplifying t = 2.588834765Subproblem 2
t + 6.25 = -8.838834765 Simplifying t + 6.25 = -8.838834765 Reorder the terms: 6.25 + t = -8.838834765 Solving 6.25 + t = -8.838834765 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 = -8.838834765 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + t = -8.838834765 + -6.25 t = -8.838834765 + -6.25 Combine like terms: -8.838834765 + -6.25 = -15.088834765 t = -15.088834765 Simplifying t = -15.088834765Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.588834765, -15.088834765}
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