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Simplifying 0.6t2 = 3t + 200 Reorder the terms: 0.6t2 = 200 + 3t Solving 0.6t2 = 200 + 3t Solving for variable 't'. Reorder the terms: -200 + -3t + 0.6t2 = 200 + 3t + -200 + -3t Reorder the terms: -200 + -3t + 0.6t2 = 200 + -200 + 3t + -3t Combine like terms: 200 + -200 = 0 -200 + -3t + 0.6t2 = 0 + 3t + -3t -200 + -3t + 0.6t2 = 3t + -3t Combine like terms: 3t + -3t = 0 -200 + -3t + 0.6t2 = 0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -333.3333333 + -5t + t2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + -5t + 333.3333333 + t2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + -5t + t2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + -5t + t2 = 0 + 333.3333333 -5t + t2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 -5t + t2 = 333.3333333 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 333.3333333 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 333.3333333 + 6.25 Combine like terms: 333.3333333 + 6.25 = 339.5833333 6.25 + -5t + t2 = 339.5833333 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 339.5833333 Calculate the square root of the right side: 18.427786989 Break this problem into two subproblems by setting (t + -2.5) equal to 18.427786989 and -18.427786989.Subproblem 1
t + -2.5 = 18.427786989 Simplifying t + -2.5 = 18.427786989 Reorder the terms: -2.5 + t = 18.427786989 Solving -2.5 + t = 18.427786989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 18.427786989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 18.427786989 + 2.5 t = 18.427786989 + 2.5 Combine like terms: 18.427786989 + 2.5 = 20.927786989 t = 20.927786989 Simplifying t = 20.927786989Subproblem 2
t + -2.5 = -18.427786989 Simplifying t + -2.5 = -18.427786989 Reorder the terms: -2.5 + t = -18.427786989 Solving -2.5 + t = -18.427786989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -18.427786989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -18.427786989 + 2.5 t = -18.427786989 + 2.5 Combine like terms: -18.427786989 + 2.5 = -15.927786989 t = -15.927786989 Simplifying t = -15.927786989Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.927786989, -15.927786989}
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