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Simplifying 0 = -16t2 + 5t + 2.5 Reorder the terms: 0 = 2.5 + 5t + -16t2 Solving 0 = 2.5 + 5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -5t + 16t2 = 2.5 + 5t + -16t2 + -2.5 + -5t + 16t2 Reorder the terms: -2.5 + -5t + 16t2 = 2.5 + -2.5 + 5t + -5t + -16t2 + 16t2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -5t + 16t2 = 0.0 + 5t + -5t + -16t2 + 16t2 -2.5 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -2.5 + -5t + 16t2 = 0 + -16t2 + 16t2 -2.5 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2.5 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.15625 + -0.3125t + t2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + -0.3125t + 0.15625 + t2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + -0.3125t + t2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + -0.3125t + t2 = 0 + 0.15625 -0.3125t + t2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 -0.3125t + t2 = 0.15625 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 0.15625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 0.15625 + 0.0244140625 Combine like terms: 0.15625 + 0.0244140625 = 0.1806640625 0.0244140625 + -0.3125t + t2 = 0.1806640625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 0.1806640625 Calculate the square root of the right side: 0.425045953 Break this problem into two subproblems by setting (t + -0.15625) equal to 0.425045953 and -0.425045953.Subproblem 1
t + -0.15625 = 0.425045953 Simplifying t + -0.15625 = 0.425045953 Reorder the terms: -0.15625 + t = 0.425045953 Solving -0.15625 + t = 0.425045953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 0.425045953 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 0.425045953 + 0.15625 t = 0.425045953 + 0.15625 Combine like terms: 0.425045953 + 0.15625 = 0.581295953 t = 0.581295953 Simplifying t = 0.581295953Subproblem 2
t + -0.15625 = -0.425045953 Simplifying t + -0.15625 = -0.425045953 Reorder the terms: -0.15625 + t = -0.425045953 Solving -0.15625 + t = -0.425045953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -0.425045953 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -0.425045953 + 0.15625 t = -0.425045953 + 0.15625 Combine like terms: -0.425045953 + 0.15625 = -0.268795953 t = -0.268795953 Simplifying t = -0.268795953Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.581295953, -0.268795953}
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