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Simplifying 4.9t2 + -5.2t + -38 = 0 Reorder the terms: -38 + -5.2t + 4.9t2 = 0 Solving -38 + -5.2t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -7.755102041 + -1.06122449t + t2 = 0 Move the constant term to the right: Add '7.755102041' to each side of the equation. -7.755102041 + -1.06122449t + 7.755102041 + t2 = 0 + 7.755102041 Reorder the terms: -7.755102041 + 7.755102041 + -1.06122449t + t2 = 0 + 7.755102041 Combine like terms: -7.755102041 + 7.755102041 = 0.000000000 0.000000000 + -1.06122449t + t2 = 0 + 7.755102041 -1.06122449t + t2 = 0 + 7.755102041 Combine like terms: 0 + 7.755102041 = 7.755102041 -1.06122449t + t2 = 7.755102041 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 = 7.755102041 + 0.2815493545 Reorder the terms: 0.2815493545 + -1.06122449t + t2 = 7.755102041 + 0.2815493545 Combine like terms: 7.755102041 + 0.2815493545 = 8.0366513955 0.2815493545 + -1.06122449t + t2 = 8.0366513955 Factor a perfect square on the left side: (t + -0.530612245)(t + -0.530612245) = 8.0366513955 Calculate the square root of the right side: 2.834898833 Break this problem into two subproblems by setting (t + -0.530612245) equal to 2.834898833 and -2.834898833.Subproblem 1
t + -0.530612245 = 2.834898833 Simplifying t + -0.530612245 = 2.834898833 Reorder the terms: -0.530612245 + t = 2.834898833 Solving -0.530612245 + t = 2.834898833 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 = 2.834898833 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + t = 2.834898833 + 0.530612245 t = 2.834898833 + 0.530612245 Combine like terms: 2.834898833 + 0.530612245 = 3.365511078 t = 3.365511078 Simplifying t = 3.365511078Subproblem 2
t + -0.530612245 = -2.834898833 Simplifying t + -0.530612245 = -2.834898833 Reorder the terms: -0.530612245 + t = -2.834898833 Solving -0.530612245 + t = -2.834898833 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 = -2.834898833 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + t = -2.834898833 + 0.530612245 t = -2.834898833 + 0.530612245 Combine like terms: -2.834898833 + 0.530612245 = -2.304286588 t = -2.304286588 Simplifying t = -2.304286588Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.365511078, -2.304286588}
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