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Simplifying (2t2 + t) = 0.0379 Reorder the terms: (t + 2t2) = 0.0379 Remove parenthesis around (t + 2t2) t + 2t2 = 0.0379 Solving t + 2t2 = 0.0379 Solving for variable 't'. Reorder the terms: -0.0379 + t + 2t2 = 0.0379 + -0.0379 Combine like terms: 0.0379 + -0.0379 = 0.0000 -0.0379 + t + 2t2 = 0.0000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.01895 + 0.5t + t2 = 0.0000 Move the constant term to the right: Add '0.01895' to each side of the equation. -0.01895 + 0.5t + 0.01895 + t2 = 0.0000 + 0.01895 Reorder the terms: -0.01895 + 0.01895 + 0.5t + t2 = 0.0000 + 0.01895 Combine like terms: -0.01895 + 0.01895 = 0.00000 0.00000 + 0.5t + t2 = 0.0000 + 0.01895 0.5t + t2 = 0.0000 + 0.01895 Combine like terms: 0.0000 + 0.01895 = 0.01895 0.5t + t2 = 0.01895 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5t + 0.25 + t2 = 0.01895 + 0.25 Reorder the terms: 0.25 + 0.5t + t2 = 0.01895 + 0.25 Combine like terms: 0.01895 + 0.25 = 0.26895 0.25 + 0.5t + t2 = 0.26895 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.26895 Calculate the square root of the right side: 0.518603895 Break this problem into two subproblems by setting (t + 0.5) equal to 0.518603895 and -0.518603895.Subproblem 1
t + 0.5 = 0.518603895 Simplifying t + 0.5 = 0.518603895 Reorder the terms: 0.5 + t = 0.518603895 Solving 0.5 + t = 0.518603895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.518603895 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.518603895 + -0.5 t = 0.518603895 + -0.5 Combine like terms: 0.518603895 + -0.5 = 0.018603895 t = 0.018603895 Simplifying t = 0.018603895Subproblem 2
t + 0.5 = -0.518603895 Simplifying t + 0.5 = -0.518603895 Reorder the terms: 0.5 + t = -0.518603895 Solving 0.5 + t = -0.518603895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.518603895 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.518603895 + -0.5 t = -0.518603895 + -0.5 Combine like terms: -0.518603895 + -0.5 = -1.018603895 t = -1.018603895 Simplifying t = -1.018603895Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.018603895, -1.018603895}
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