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Simplifying 2t2 + 27t + 4 = 0 Reorder the terms: 4 + 27t + 2t2 = 0 Solving 4 + 27t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 13.5t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 13.5t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 13.5t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 13.5t + t2 = 0 + -2 13.5t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 13.5t + t2 = -2 The t term is 13.5t. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5t + 45.5625 + t2 = -2 + 45.5625 Reorder the terms: 45.5625 + 13.5t + t2 = -2 + 45.5625 Combine like terms: -2 + 45.5625 = 43.5625 45.5625 + 13.5t + t2 = 43.5625 Factor a perfect square on the left side: (t + 6.75)(t + 6.75) = 43.5625 Calculate the square root of the right side: 6.600189391 Break this problem into two subproblems by setting (t + 6.75) equal to 6.600189391 and -6.600189391.Subproblem 1
t + 6.75 = 6.600189391 Simplifying t + 6.75 = 6.600189391 Reorder the terms: 6.75 + t = 6.600189391 Solving 6.75 + t = 6.600189391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + t = 6.600189391 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + t = 6.600189391 + -6.75 t = 6.600189391 + -6.75 Combine like terms: 6.600189391 + -6.75 = -0.149810609 t = -0.149810609 Simplifying t = -0.149810609Subproblem 2
t + 6.75 = -6.600189391 Simplifying t + 6.75 = -6.600189391 Reorder the terms: 6.75 + t = -6.600189391 Solving 6.75 + t = -6.600189391 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + t = -6.600189391 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + t = -6.600189391 + -6.75 t = -6.600189391 + -6.75 Combine like terms: -6.600189391 + -6.75 = -13.350189391 t = -13.350189391 Simplifying t = -13.350189391Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.149810609, -13.350189391}
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