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Simplifying 4.9t2 + 15t + -35 = 0 Reorder the terms: -35 + 15t + 4.9t2 = 0 Solving -35 + 15t + 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'. -7.142857143 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 3.06122449t + 7.142857143 + t2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 3.06122449t + t2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 3.06122449t + t2 = 0 + 7.142857143 3.06122449t + t2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 3.06122449t + t2 = 7.142857143 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 = 7.142857143 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 7.142857143 + 2.342773845 Combine like terms: 7.142857143 + 2.342773845 = 9.485630988 2.342773845 + 3.06122449t + t2 = 9.485630988 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 9.485630988 Calculate the square root of the right side: 3.079875158 Break this problem into two subproblems by setting (t + 1.530612245) equal to 3.079875158 and -3.079875158.Subproblem 1
t + 1.530612245 = 3.079875158 Simplifying t + 1.530612245 = 3.079875158 Reorder the terms: 1.530612245 + t = 3.079875158 Solving 1.530612245 + t = 3.079875158 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 = 3.079875158 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 3.079875158 + -1.530612245 t = 3.079875158 + -1.530612245 Combine like terms: 3.079875158 + -1.530612245 = 1.549262913 t = 1.549262913 Simplifying t = 1.549262913Subproblem 2
t + 1.530612245 = -3.079875158 Simplifying t + 1.530612245 = -3.079875158 Reorder the terms: 1.530612245 + t = -3.079875158 Solving 1.530612245 + t = -3.079875158 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 = -3.079875158 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -3.079875158 + -1.530612245 t = -3.079875158 + -1.530612245 Combine like terms: -3.079875158 + -1.530612245 = -4.610487403 t = -4.610487403 Simplifying t = -4.610487403Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.549262913, -4.610487403}
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