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Simplifying 8 = 12t + -2.5t2 Solving 8 = 12t + -2.5t2 Solving for variable 't'. Reorder the terms: 8 + -12t + 2.5t2 = 12t + -12t + -2.5t2 + 2.5t2 Combine like terms: 12t + -12t = 0 8 + -12t + 2.5t2 = 0 + -2.5t2 + 2.5t2 8 + -12t + 2.5t2 = -2.5t2 + 2.5t2 Combine like terms: -2.5t2 + 2.5t2 = 0.0 8 + -12t + 2.5t2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 3.2 + -4.8t + t2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -4.8t + -3.2 + t2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -4.8t + t2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -4.8t + t2 = 0 + -3.2 -4.8t + t2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -4.8t + t2 = -3.2 The t term is -4.8t. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8t + 5.76 + t2 = -3.2 + 5.76 Reorder the terms: 5.76 + -4.8t + t2 = -3.2 + 5.76 Combine like terms: -3.2 + 5.76 = 2.56 5.76 + -4.8t + t2 = 2.56 Factor a perfect square on the left side: (t + -2.4)(t + -2.4) = 2.56 Calculate the square root of the right side: 1.6 Break this problem into two subproblems by setting (t + -2.4) equal to 1.6 and -1.6.Subproblem 1
t + -2.4 = 1.6 Simplifying t + -2.4 = 1.6 Reorder the terms: -2.4 + t = 1.6 Solving -2.4 + t = 1.6 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = 1.6 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = 1.6 + 2.4 t = 1.6 + 2.4 Combine like terms: 1.6 + 2.4 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -2.4 = -1.6 Simplifying t + -2.4 = -1.6 Reorder the terms: -2.4 + t = -1.6 Solving -2.4 + t = -1.6 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = -1.6 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = -1.6 + 2.4 t = -1.6 + 2.4 Combine like terms: -1.6 + 2.4 = 0.8 t = 0.8 Simplifying t = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, 0.8}
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