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Simplifying 25 = 16t2 + 15t Reorder the terms: 25 = 15t + 16t2 Solving 25 = 15t + 16t2 Solving for variable 't'. Reorder the terms: 25 + -15t + -16t2 = 15t + -15t + 16t2 + -16t2 Combine like terms: 15t + -15t = 0 25 + -15t + -16t2 = 0 + 16t2 + -16t2 25 + -15t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 25 + -15t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.5625 + 0.9375t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.9375t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.9375t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.9375t + t2 = 0 + 1.5625 0.9375t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.9375t + t2 = 1.5625 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = 1.5625 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 1.5625 + 0.2197265625 Combine like terms: 1.5625 + 0.2197265625 = 1.7822265625 0.2197265625 + 0.9375t + t2 = 1.7822265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 1.7822265625 Calculate the square root of the right side: 1.335000585 Break this problem into two subproblems by setting (t + 0.46875) equal to 1.335000585 and -1.335000585.Subproblem 1
t + 0.46875 = 1.335000585 Simplifying t + 0.46875 = 1.335000585 Reorder the terms: 0.46875 + t = 1.335000585 Solving 0.46875 + t = 1.335000585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 1.335000585 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 1.335000585 + -0.46875 t = 1.335000585 + -0.46875 Combine like terms: 1.335000585 + -0.46875 = 0.866250585 t = 0.866250585 Simplifying t = 0.866250585Subproblem 2
t + 0.46875 = -1.335000585 Simplifying t + 0.46875 = -1.335000585 Reorder the terms: 0.46875 + t = -1.335000585 Solving 0.46875 + t = -1.335000585 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -1.335000585 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -1.335000585 + -0.46875 t = -1.335000585 + -0.46875 Combine like terms: -1.335000585 + -0.46875 = -1.803750585 t = -1.803750585 Simplifying t = -1.803750585Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.866250585, -1.803750585}
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