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Simplifying -4.9t2 + -1.5t + 41 = 0 Reorder the terms: 41 + -1.5t + -4.9t2 = 0 Solving 41 + -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'. -8.367346939 + 0.306122449t + t2 = 0 Move the constant term to the right: Add '8.367346939' to each side of the equation. -8.367346939 + 0.306122449t + 8.367346939 + t2 = 0 + 8.367346939 Reorder the terms: -8.367346939 + 8.367346939 + 0.306122449t + t2 = 0 + 8.367346939 Combine like terms: -8.367346939 + 8.367346939 = 0.000000000 0.000000000 + 0.306122449t + t2 = 0 + 8.367346939 0.306122449t + t2 = 0 + 8.367346939 Combine like terms: 0 + 8.367346939 = 8.367346939 0.306122449t + t2 = 8.367346939 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 = 8.367346939 + 0.02342773845 Reorder the terms: 0.02342773845 + 0.306122449t + t2 = 8.367346939 + 0.02342773845 Combine like terms: 8.367346939 + 0.02342773845 = 8.39077467745 0.02342773845 + 0.306122449t + t2 = 8.39077467745 Factor a perfect square on the left side: (t + 0.1530612245)(t + 0.1530612245) = 8.39077467745 Calculate the square root of the right side: 2.896683393 Break this problem into two subproblems by setting (t + 0.1530612245) equal to 2.896683393 and -2.896683393.Subproblem 1
t + 0.1530612245 = 2.896683393 Simplifying t + 0.1530612245 = 2.896683393 Reorder the terms: 0.1530612245 + t = 2.896683393 Solving 0.1530612245 + t = 2.896683393 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 = 2.896683393 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = 2.896683393 + -0.1530612245 t = 2.896683393 + -0.1530612245 Combine like terms: 2.896683393 + -0.1530612245 = 2.7436221685 t = 2.7436221685 Simplifying t = 2.7436221685Subproblem 2
t + 0.1530612245 = -2.896683393 Simplifying t + 0.1530612245 = -2.896683393 Reorder the terms: 0.1530612245 + t = -2.896683393 Solving 0.1530612245 + t = -2.896683393 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 = -2.896683393 + -0.1530612245 Combine like terms: 0.1530612245 + -0.1530612245 = 0.0000000000 0.0000000000 + t = -2.896683393 + -0.1530612245 t = -2.896683393 + -0.1530612245 Combine like terms: -2.896683393 + -0.1530612245 = -3.0497446175 t = -3.0497446175 Simplifying t = -3.0497446175Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.7436221685, -3.0497446175}
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