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Simplifying 184 = 120 + 6t + 0.04t2 Solving 184 = 120 + 6t + 0.04t2 Solving for variable 't'. Combine like terms: 184 + -120 = 64 64 + -6t + -0.04t2 = 120 + 6t + 0.04t2 + -120 + -6t + -0.04t2 Reorder the terms: 64 + -6t + -0.04t2 = 120 + -120 + 6t + -6t + 0.04t2 + -0.04t2 Combine like terms: 120 + -120 = 0 64 + -6t + -0.04t2 = 0 + 6t + -6t + 0.04t2 + -0.04t2 64 + -6t + -0.04t2 = 6t + -6t + 0.04t2 + -0.04t2 Combine like terms: 6t + -6t = 0 64 + -6t + -0.04t2 = 0 + 0.04t2 + -0.04t2 64 + -6t + -0.04t2 = 0.04t2 + -0.04t2 Combine like terms: 0.04t2 + -0.04t2 = 0.00 64 + -6t + -0.04t2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -1600 + 150t + t2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 150t + 1600 + t2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 150t + t2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 150t + t2 = 0 + 1600 150t + t2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 150t + t2 = 1600 The t term is 150t. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150t + 5625 + t2 = 1600 + 5625 Reorder the terms: 5625 + 150t + t2 = 1600 + 5625 Combine like terms: 1600 + 5625 = 7225 5625 + 150t + t2 = 7225 Factor a perfect square on the left side: (t + 75)(t + 75) = 7225 Calculate the square root of the right side: 85 Break this problem into two subproblems by setting (t + 75) equal to 85 and -85.Subproblem 1
t + 75 = 85 Simplifying t + 75 = 85 Reorder the terms: 75 + t = 85 Solving 75 + t = 85 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + t = 85 + -75 Combine like terms: 75 + -75 = 0 0 + t = 85 + -75 t = 85 + -75 Combine like terms: 85 + -75 = 10 t = 10 Simplifying t = 10Subproblem 2
t + 75 = -85 Simplifying t + 75 = -85 Reorder the terms: 75 + t = -85 Solving 75 + t = -85 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + t = -85 + -75 Combine like terms: 75 + -75 = 0 0 + t = -85 + -75 t = -85 + -75 Combine like terms: -85 + -75 = -160 t = -160 Simplifying t = -160Solution
The solution to the problem is based on the solutions from the subproblems. t = {10, -160}
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