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Simplifying 0.05t2 + -5t + -8 = 0 Reorder the terms: -8 + -5t + 0.05t2 = 0 Solving -8 + -5t + 0.05t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -160 + -100t + t2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -100t + 160 + t2 = 0 + 160 Reorder the terms: -160 + 160 + -100t + t2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -100t + t2 = 0 + 160 -100t + t2 = 0 + 160 Combine like terms: 0 + 160 = 160 -100t + t2 = 160 The t term is -100t. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100t + 2500 + t2 = 160 + 2500 Reorder the terms: 2500 + -100t + t2 = 160 + 2500 Combine like terms: 160 + 2500 = 2660 2500 + -100t + t2 = 2660 Factor a perfect square on the left side: (t + -50)(t + -50) = 2660 Calculate the square root of the right side: 51.575187833 Break this problem into two subproblems by setting (t + -50) equal to 51.575187833 and -51.575187833.Subproblem 1
t + -50 = 51.575187833 Simplifying t + -50 = 51.575187833 Reorder the terms: -50 + t = 51.575187833 Solving -50 + t = 51.575187833 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = 51.575187833 + 50 Combine like terms: -50 + 50 = 0 0 + t = 51.575187833 + 50 t = 51.575187833 + 50 Combine like terms: 51.575187833 + 50 = 101.575187833 t = 101.575187833 Simplifying t = 101.575187833Subproblem 2
t + -50 = -51.575187833 Simplifying t + -50 = -51.575187833 Reorder the terms: -50 + t = -51.575187833 Solving -50 + t = -51.575187833 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = -51.575187833 + 50 Combine like terms: -50 + 50 = 0 0 + t = -51.575187833 + 50 t = -51.575187833 + 50 Combine like terms: -51.575187833 + 50 = -1.575187833 t = -1.575187833 Simplifying t = -1.575187833Solution
The solution to the problem is based on the solutions from the subproblems. t = {101.575187833, -1.575187833}
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