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Simplifying 25 = -2t2 + 16t + 0.5 Reorder the terms: 25 = 0.5 + 16t + -2t2 Solving 25 = 0.5 + 16t + -2t2 Solving for variable 't'. Combine like terms: 25 + -0.5 = 24.5 24.5 + -16t + 2t2 = 0.5 + 16t + -2t2 + -0.5 + -16t + 2t2 Reorder the terms: 24.5 + -16t + 2t2 = 0.5 + -0.5 + 16t + -16t + -2t2 + 2t2 Combine like terms: 0.5 + -0.5 = 0.0 24.5 + -16t + 2t2 = 0.0 + 16t + -16t + -2t2 + 2t2 24.5 + -16t + 2t2 = 16t + -16t + -2t2 + 2t2 Combine like terms: 16t + -16t = 0 24.5 + -16t + 2t2 = 0 + -2t2 + 2t2 24.5 + -16t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 24.5 + -16t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.25 + -8t + t2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -8t + -12.25 + t2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -8t + t2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -8t + t2 = 0 + -12.25 -8t + t2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -8t + t2 = -12.25 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -12.25 + 16 Reorder the terms: 16 + -8t + t2 = -12.25 + 16 Combine like terms: -12.25 + 16 = 3.75 16 + -8t + t2 = 3.75 Factor a perfect square on the left side: (t + -4)(t + -4) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (t + -4) equal to 1.936491673 and -1.936491673.Subproblem 1
t + -4 = 1.936491673 Simplifying t + -4 = 1.936491673 Reorder the terms: -4 + t = 1.936491673 Solving -4 + t = 1.936491673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 1.936491673 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.936491673 + 4 t = 1.936491673 + 4 Combine like terms: 1.936491673 + 4 = 5.936491673 t = 5.936491673 Simplifying t = 5.936491673Subproblem 2
t + -4 = -1.936491673 Simplifying t + -4 = -1.936491673 Reorder the terms: -4 + t = -1.936491673 Solving -4 + t = -1.936491673 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -1.936491673 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.936491673 + 4 t = -1.936491673 + 4 Combine like terms: -1.936491673 + 4 = 2.063508327 t = 2.063508327 Simplifying t = 2.063508327Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.936491673, 2.063508327}
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