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Simplifying 16t2 + 40t = 25 Reorder the terms: 40t + 16t2 = 25 Solving 40t + 16t2 = 25 Solving for variable 't'. Reorder the terms: -25 + 40t + 16t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 40t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 2.5t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 2.5t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 2.5t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 2.5t + t2 = 0 + 1.5625 2.5t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 2.5t + t2 = 1.5625 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 1.5625 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 1.5625 + 1.5625 Combine like terms: 1.5625 + 1.5625 = 3.125 1.5625 + 2.5t + t2 = 3.125 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (t + 1.25) equal to 1.767766953 and -1.767766953.Subproblem 1
t + 1.25 = 1.767766953 Simplifying t + 1.25 = 1.767766953 Reorder the terms: 1.25 + t = 1.767766953 Solving 1.25 + t = 1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 1.767766953 + -1.25 t = 1.767766953 + -1.25 Combine like terms: 1.767766953 + -1.25 = 0.517766953 t = 0.517766953 Simplifying t = 0.517766953Subproblem 2
t + 1.25 = -1.767766953 Simplifying t + 1.25 = -1.767766953 Reorder the terms: 1.25 + t = -1.767766953 Solving 1.25 + t = -1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -1.767766953 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -1.767766953 + -1.25 t = -1.767766953 + -1.25 Combine like terms: -1.767766953 + -1.25 = -3.017766953 t = -3.017766953 Simplifying t = -3.017766953Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.517766953, -3.017766953}
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