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Simplifying 4.9t2 + 1.5t + -60 = 0 Reorder the terms: -60 + 1.5t + 4.9t2 = 0 Solving -60 + 1.5t + 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'. -12.24489796 + 0.306122449t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 0.306122449t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 0.306122449t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 0.306122449t + t2 = 0 + 12.24489796 0.306122449t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 0.306122449t + t2 = 12.24489796 The t term is 0.306122449t. Take half its coefficient (0.1530612245). Square it (0.02342773845) and add it to both sides. Add '0.02342773845' to each side of the equation. 0.306122449t + 0.02342773845 + t2 = 12.24489796 + 0.02342773845 Reorder the terms: 0.02342773845 + 0.306122449t + t2 = 12.24489796 + 0.02342773845 Combine like terms: 12.24489796 + 0.02342773845 = 12.26832569845 0.02342773845 + 0.306122449t + t2 = 12.26832569845 Factor a perfect square on the left side: (t + 0.1530612245)(t + 0.1530612245) = 12.26832569845 Calculate the square root of the right side: 3.502616979 Break this problem into two subproblems by setting (t + 0.1530612245) equal to 3.502616979 and -3.502616979.Subproblem 1
t + 0.1530612245 = 3.502616979 Simplifying t + 0.1530612245 = 3.502616979 Reorder the terms: 0.1530612245 + t = 3.502616979 Solving 0.1530612245 + t = 3.502616979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1530612245' to each side of the equation. 0.1530612245 + -0.1530612245 + t = 3.502616979 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = 3.502616979 + -0.1530612245 t = 3.502616979 + -0.1530612245 Combine like terms: 3.502616979 + -0.1530612245 = 3.3495557545 t = 3.3495557545 Simplifying t = 3.3495557545Subproblem 2
t + 0.1530612245 = -3.502616979 Simplifying t + 0.1530612245 = -3.502616979 Reorder the terms: 0.1530612245 + t = -3.502616979 Solving 0.1530612245 + t = -3.502616979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1530612245' to each side of the equation. 0.1530612245 + -0.1530612245 + t = -3.502616979 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = -3.502616979 + -0.1530612245 t = -3.502616979 + -0.1530612245 Combine like terms: -3.502616979 + -0.1530612245 = -3.6556782035 t = -3.6556782035 Simplifying t = -3.6556782035Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.3495557545, -3.6556782035}
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