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Simplifying 2(t) = -0.8t2 + 24t + 8 Reorder the terms: 2t = 8 + 24t + -0.8t2 Solving 2t = 8 + 24t + -0.8t2 Solving for variable 't'. Reorder the terms: -8 + 2t + -24t + 0.8t2 = 8 + 24t + -0.8t2 + -8 + -24t + 0.8t2 Combine like terms: 2t + -24t = -22t -8 + -22t + 0.8t2 = 8 + 24t + -0.8t2 + -8 + -24t + 0.8t2 Reorder the terms: -8 + -22t + 0.8t2 = 8 + -8 + 24t + -24t + -0.8t2 + 0.8t2 Combine like terms: 8 + -8 = 0 -8 + -22t + 0.8t2 = 0 + 24t + -24t + -0.8t2 + 0.8t2 -8 + -22t + 0.8t2 = 24t + -24t + -0.8t2 + 0.8t2 Combine like terms: 24t + -24t = 0 -8 + -22t + 0.8t2 = 0 + -0.8t2 + 0.8t2 -8 + -22t + 0.8t2 = -0.8t2 + 0.8t2 Combine like terms: -0.8t2 + 0.8t2 = 0.0 -8 + -22t + 0.8t2 = 0.0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -10 + -27.5t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -27.5t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -27.5t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -27.5t + t2 = 0 + 10 -27.5t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -27.5t + t2 = 10 The t term is -27.5t. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5t + 189.0625 + t2 = 10 + 189.0625 Reorder the terms: 189.0625 + -27.5t + t2 = 10 + 189.0625 Combine like terms: 10 + 189.0625 = 199.0625 189.0625 + -27.5t + t2 = 199.0625 Factor a perfect square on the left side: (t + -13.75)(t + -13.75) = 199.0625 Calculate the square root of the right side: 14.10895106 Break this problem into two subproblems by setting (t + -13.75) equal to 14.10895106 and -14.10895106.Subproblem 1
t + -13.75 = 14.10895106 Simplifying t + -13.75 = 14.10895106 Reorder the terms: -13.75 + t = 14.10895106 Solving -13.75 + t = 14.10895106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = 14.10895106 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = 14.10895106 + 13.75 t = 14.10895106 + 13.75 Combine like terms: 14.10895106 + 13.75 = 27.85895106 t = 27.85895106 Simplifying t = 27.85895106Subproblem 2
t + -13.75 = -14.10895106 Simplifying t + -13.75 = -14.10895106 Reorder the terms: -13.75 + t = -14.10895106 Solving -13.75 + t = -14.10895106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = -14.10895106 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = -14.10895106 + 13.75 t = -14.10895106 + 13.75 Combine like terms: -14.10895106 + 13.75 = -0.35895106 t = -0.35895106 Simplifying t = -0.35895106Solution
The solution to the problem is based on the solutions from the subproblems. t = {27.85895106, -0.35895106}
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