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Simplifying -2 = 15t + 4.9t2 Solving -2 = 15t + 4.9t2 Solving for variable 't'. Reorder the terms: -2 + -15t + -4.9t2 = 15t + -15t + 4.9t2 + -4.9t2 Combine like terms: 15t + -15t = 0 -2 + -15t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -2 + -15t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -2 + -15t + -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'. 0.4081632653 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + 3.06122449t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + 3.06122449t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + 3.06122449t + t2 = 0 + -0.4081632653 3.06122449t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 3.06122449t + t2 = -0.4081632653 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 = -0.4081632653 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = -0.4081632653 + 2.342773845 Combine like terms: -0.4081632653 + 2.342773845 = 1.9346105797 2.342773845 + 3.06122449t + t2 = 1.9346105797 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 1.9346105797 Calculate the square root of the right side: 1.390902793 Break this problem into two subproblems by setting (t + 1.530612245) equal to 1.390902793 and -1.390902793.Subproblem 1
t + 1.530612245 = 1.390902793 Simplifying t + 1.530612245 = 1.390902793 Reorder the terms: 1.530612245 + t = 1.390902793 Solving 1.530612245 + t = 1.390902793 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 = 1.390902793 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 1.390902793 + -1.530612245 t = 1.390902793 + -1.530612245 Combine like terms: 1.390902793 + -1.530612245 = -0.139709452 t = -0.139709452 Simplifying t = -0.139709452Subproblem 2
t + 1.530612245 = -1.390902793 Simplifying t + 1.530612245 = -1.390902793 Reorder the terms: 1.530612245 + t = -1.390902793 Solving 1.530612245 + t = -1.390902793 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 = -1.390902793 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -1.390902793 + -1.530612245 t = -1.390902793 + -1.530612245 Combine like terms: -1.390902793 + -1.530612245 = -2.921515038 t = -2.921515038 Simplifying t = -2.921515038Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.139709452, -2.921515038}
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