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Simplifying 0 = 125 + 5.2t + -4.9t2 Solving 0 = 125 + 5.2t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -125 = -125 -125 + -5.2t + 4.9t2 = 125 + 5.2t + -4.9t2 + -125 + -5.2t + 4.9t2 Reorder the terms: -125 + -5.2t + 4.9t2 = 125 + -125 + 5.2t + -5.2t + -4.9t2 + 4.9t2 Combine like terms: 125 + -125 = 0 -125 + -5.2t + 4.9t2 = 0 + 5.2t + -5.2t + -4.9t2 + 4.9t2 -125 + -5.2t + 4.9t2 = 5.2t + -5.2t + -4.9t2 + 4.9t2 Combine like terms: 5.2t + -5.2t = 0.0 -125 + -5.2t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -125 + -5.2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -125 + -5.2t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -25.51020408 + -1.06122449t + t2 = 0 Move the constant term to the right: Add '25.51020408' to each side of the equation. -25.51020408 + -1.06122449t + 25.51020408 + t2 = 0 + 25.51020408 Reorder the terms: -25.51020408 + 25.51020408 + -1.06122449t + t2 = 0 + 25.51020408 Combine like terms: -25.51020408 + 25.51020408 = 0.00000000 0.00000000 + -1.06122449t + t2 = 0 + 25.51020408 -1.06122449t + t2 = 0 + 25.51020408 Combine like terms: 0 + 25.51020408 = 25.51020408 -1.06122449t + t2 = 25.51020408 The t term is -1.06122449t. Take half its coefficient (-0.530612245). Square it (0.2815493545) and add it to both sides. Add '0.2815493545' to each side of the equation. -1.06122449t + 0.2815493545 + t2 = 25.51020408 + 0.2815493545 Reorder the terms: 0.2815493545 + -1.06122449t + t2 = 25.51020408 + 0.2815493545 Combine like terms: 25.51020408 + 0.2815493545 = 25.7917534345 0.2815493545 + -1.06122449t + t2 = 25.7917534345 Factor a perfect square on the left side: (t + -0.530612245)(t + -0.530612245) = 25.7917534345 Calculate the square root of the right side: 5.078558204 Break this problem into two subproblems by setting (t + -0.530612245) equal to 5.078558204 and -5.078558204.Subproblem 1
t + -0.530612245 = 5.078558204 Simplifying t + -0.530612245 = 5.078558204 Reorder the terms: -0.530612245 + t = 5.078558204 Solving -0.530612245 + t = 5.078558204 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + t = 5.078558204 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + t = 5.078558204 + 0.530612245 t = 5.078558204 + 0.530612245 Combine like terms: 5.078558204 + 0.530612245 = 5.609170449 t = 5.609170449 Simplifying t = 5.609170449Subproblem 2
t + -0.530612245 = -5.078558204 Simplifying t + -0.530612245 = -5.078558204 Reorder the terms: -0.530612245 + t = -5.078558204 Solving -0.530612245 + t = -5.078558204 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + t = -5.078558204 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + t = -5.078558204 + 0.530612245 t = -5.078558204 + 0.530612245 Combine like terms: -5.078558204 + 0.530612245 = -4.547945959 t = -4.547945959 Simplifying t = -4.547945959Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.609170449, -4.547945959}
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