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Simplifying 9.8t2 + 30t = 50 Reorder the terms: 30t + 9.8t2 = 50 Solving 30t + 9.8t2 = 50 Solving for variable 't'. Reorder the terms: -50 + 30t + 9.8t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 30t + 9.8t2 = 0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -5.102040816 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + 3.06122449t + 5.102040816 + t2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + 3.06122449t + t2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + 3.06122449t + t2 = 0 + 5.102040816 3.06122449t + t2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 3.06122449t + t2 = 5.102040816 The t term is 3.06122449t. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449t + 2.342773845 + t2 = 5.102040816 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 5.102040816 + 2.342773845 Combine like terms: 5.102040816 + 2.342773845 = 7.444814661 2.342773845 + 3.06122449t + t2 = 7.444814661 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 7.444814661 Calculate the square root of the right side: 2.728518767 Break this problem into two subproblems by setting (t + 1.530612245) equal to 2.728518767 and -2.728518767.Subproblem 1
t + 1.530612245 = 2.728518767 Simplifying t + 1.530612245 = 2.728518767 Reorder the terms: 1.530612245 + t = 2.728518767 Solving 1.530612245 + t = 2.728518767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = 2.728518767 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 2.728518767 + -1.530612245 t = 2.728518767 + -1.530612245 Combine like terms: 2.728518767 + -1.530612245 = 1.197906522 t = 1.197906522 Simplifying t = 1.197906522Subproblem 2
t + 1.530612245 = -2.728518767 Simplifying t + 1.530612245 = -2.728518767 Reorder the terms: 1.530612245 + t = -2.728518767 Solving 1.530612245 + t = -2.728518767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = -2.728518767 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -2.728518767 + -1.530612245 t = -2.728518767 + -1.530612245 Combine like terms: -2.728518767 + -1.530612245 = -4.259131012 t = -4.259131012 Simplifying t = -4.259131012Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.197906522, -4.259131012}
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