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Simplifying -4.9t2 + 15t + -6 = 0 Reorder the terms: -6 + 15t + -4.9t2 = 0 Solving -6 + 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'. 1.224489796 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '-1.224489796' to each side of the equation. 1.224489796 + -3.06122449t + -1.224489796 + t2 = 0 + -1.224489796 Reorder the terms: 1.224489796 + -1.224489796 + -3.06122449t + t2 = 0 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + -3.06122449t + t2 = 0 + -1.224489796 -3.06122449t + t2 = 0 + -1.224489796 Combine like terms: 0 + -1.224489796 = -1.224489796 -3.06122449t + t2 = -1.224489796 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 = -1.224489796 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = -1.224489796 + 2.342773845 Combine like terms: -1.224489796 + 2.342773845 = 1.118284049 2.342773845 + -3.06122449t + t2 = 1.118284049 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 1.118284049 Calculate the square root of the right side: 1.057489503 Break this problem into two subproblems by setting (t + -1.530612245) equal to 1.057489503 and -1.057489503.Subproblem 1
t + -1.530612245 = 1.057489503 Simplifying t + -1.530612245 = 1.057489503 Reorder the terms: -1.530612245 + t = 1.057489503 Solving -1.530612245 + t = 1.057489503 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 = 1.057489503 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 1.057489503 + 1.530612245 t = 1.057489503 + 1.530612245 Combine like terms: 1.057489503 + 1.530612245 = 2.588101748 t = 2.588101748 Simplifying t = 2.588101748Subproblem 2
t + -1.530612245 = -1.057489503 Simplifying t + -1.530612245 = -1.057489503 Reorder the terms: -1.530612245 + t = -1.057489503 Solving -1.530612245 + t = -1.057489503 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 = -1.057489503 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -1.057489503 + 1.530612245 t = -1.057489503 + 1.530612245 Combine like terms: -1.057489503 + 1.530612245 = 0.473122742 t = 0.473122742 Simplifying t = 0.473122742Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.588101748, 0.473122742}
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