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Simplifying 0 = -3.2t2 + 12.8t + 1 Reorder the terms: 0 = 1 + 12.8t + -3.2t2 Solving 0 = 1 + 12.8t + -3.2t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -12.8t + 3.2t2 = 1 + 12.8t + -3.2t2 + -1 + -12.8t + 3.2t2 Reorder the terms: -1 + -12.8t + 3.2t2 = 1 + -1 + 12.8t + -12.8t + -3.2t2 + 3.2t2 Combine like terms: 1 + -1 = 0 -1 + -12.8t + 3.2t2 = 0 + 12.8t + -12.8t + -3.2t2 + 3.2t2 -1 + -12.8t + 3.2t2 = 12.8t + -12.8t + -3.2t2 + 3.2t2 Combine like terms: 12.8t + -12.8t = 0.0 -1 + -12.8t + 3.2t2 = 0.0 + -3.2t2 + 3.2t2 -1 + -12.8t + 3.2t2 = -3.2t2 + 3.2t2 Combine like terms: -3.2t2 + 3.2t2 = 0.0 -1 + -12.8t + 3.2t2 = 0.0 Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -0.3125 + -4t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4t + t2 = 0 + 0.3125 -4t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4t + t2 = 0.3125 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 0.3125 + 4 Reorder the terms: 4 + -4t + t2 = 0.3125 + 4 Combine like terms: 0.3125 + 4 = 4.3125 4 + -4t + t2 = 4.3125 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (t + -2) equal to 2.076655966 and -2.076655966.Subproblem 1
t + -2 = 2.076655966 Simplifying t + -2 = 2.076655966 Reorder the terms: -2 + t = 2.076655966 Solving -2 + t = 2.076655966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.076655966 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.076655966 + 2 t = 2.076655966 + 2 Combine like terms: 2.076655966 + 2 = 4.076655966 t = 4.076655966 Simplifying t = 4.076655966Subproblem 2
t + -2 = -2.076655966 Simplifying t + -2 = -2.076655966 Reorder the terms: -2 + t = -2.076655966 Solving -2 + t = -2.076655966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.076655966 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.076655966 + 2 t = -2.076655966 + 2 Combine like terms: -2.076655966 + 2 = -0.076655966 t = -0.076655966 Simplifying t = -0.076655966Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.076655966, -0.076655966}
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