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Simplifying (t) = 20t + 2t2 + -100 t = 20t + 2t2 + -100 Reorder the terms: t = -100 + 20t + 2t2 Solving t = -100 + 20t + 2t2 Solving for variable 't'. Reorder the terms: 100 + t + -20t + -2t2 = -100 + 20t + 2t2 + 100 + -20t + -2t2 Combine like terms: t + -20t = -19t 100 + -19t + -2t2 = -100 + 20t + 2t2 + 100 + -20t + -2t2 Reorder the terms: 100 + -19t + -2t2 = -100 + 100 + 20t + -20t + 2t2 + -2t2 Combine like terms: -100 + 100 = 0 100 + -19t + -2t2 = 0 + 20t + -20t + 2t2 + -2t2 100 + -19t + -2t2 = 20t + -20t + 2t2 + -2t2 Combine like terms: 20t + -20t = 0 100 + -19t + -2t2 = 0 + 2t2 + -2t2 100 + -19t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 100 + -19t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -50 + 9.5t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 9.5t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + 9.5t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 9.5t + t2 = 0 + 50 9.5t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 9.5t + t2 = 50 The t term is 9.5t. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5t + 22.5625 + t2 = 50 + 22.5625 Reorder the terms: 22.5625 + 9.5t + t2 = 50 + 22.5625 Combine like terms: 50 + 22.5625 = 72.5625 22.5625 + 9.5t + t2 = 72.5625 Factor a perfect square on the left side: (t + 4.75)(t + 4.75) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (t + 4.75) equal to 8.518362519 and -8.518362519.Subproblem 1
t + 4.75 = 8.518362519 Simplifying t + 4.75 = 8.518362519 Reorder the terms: 4.75 + t = 8.518362519 Solving 4.75 + t = 8.518362519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = 8.518362519 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = 8.518362519 + -4.75 t = 8.518362519 + -4.75 Combine like terms: 8.518362519 + -4.75 = 3.768362519 t = 3.768362519 Simplifying t = 3.768362519Subproblem 2
t + 4.75 = -8.518362519 Simplifying t + 4.75 = -8.518362519 Reorder the terms: 4.75 + t = -8.518362519 Solving 4.75 + t = -8.518362519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = -8.518362519 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = -8.518362519 + -4.75 t = -8.518362519 + -4.75 Combine like terms: -8.518362519 + -4.75 = -13.268362519 t = -13.268362519 Simplifying t = -13.268362519Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.768362519, -13.268362519}
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