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Simplifying 0.5(9.8) * t2 + 15t + -45 = 0 Multiply 0.5 * 9.8 4.9t2 + 15t + -45 = 0 Reorder the terms: -45 + 15t + 4.9t2 = 0 Solving -45 + 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'. -9.183673469 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + 3.06122449t + 9.183673469 + t2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + 3.06122449t + t2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + 3.06122449t + t2 = 0 + 9.183673469 3.06122449t + t2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 3.06122449t + t2 = 9.183673469 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 = 9.183673469 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 9.183673469 + 2.342773845 Combine like terms: 9.183673469 + 2.342773845 = 11.526447314 2.342773845 + 3.06122449t + t2 = 11.526447314 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 11.526447314 Calculate the square root of the right side: 3.395062196 Break this problem into two subproblems by setting (t + 1.530612245) equal to 3.395062196 and -3.395062196.Subproblem 1
t + 1.530612245 = 3.395062196 Simplifying t + 1.530612245 = 3.395062196 Reorder the terms: 1.530612245 + t = 3.395062196 Solving 1.530612245 + t = 3.395062196 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 = 3.395062196 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 3.395062196 + -1.530612245 t = 3.395062196 + -1.530612245 Combine like terms: 3.395062196 + -1.530612245 = 1.864449951 t = 1.864449951 Simplifying t = 1.864449951Subproblem 2
t + 1.530612245 = -3.395062196 Simplifying t + 1.530612245 = -3.395062196 Reorder the terms: 1.530612245 + t = -3.395062196 Solving 1.530612245 + t = -3.395062196 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 = -3.395062196 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -3.395062196 + -1.530612245 t = -3.395062196 + -1.530612245 Combine like terms: -3.395062196 + -1.530612245 = -4.925674441 t = -4.925674441 Simplifying t = -4.925674441Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.864449951, -4.925674441}
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