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Simplifying 3t(2t + -1) = 8 Reorder the terms: 3t(-1 + 2t) = 8 (-1 * 3t + 2t * 3t) = 8 (-3t + 6t2) = 8 Solving -3t + 6t2 = 8 Solving for variable 't'. Reorder the terms: -8 + -3t + 6t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -3t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + -0.5t + t2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.5t + 1.333333333 + t2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.5t + t2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.5t + t2 = 0 + 1.333333333 -0.5t + t2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.5t + t2 = 1.333333333 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 1.333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 1.333333333 + 0.0625 Combine like terms: 1.333333333 + 0.0625 = 1.395833333 0.0625 + -0.5t + t2 = 1.395833333 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 1.395833333 Calculate the square root of the right side: 1.181453906 Break this problem into two subproblems by setting (t + -0.25) equal to 1.181453906 and -1.181453906.Subproblem 1
t + -0.25 = 1.181453906 Simplifying t + -0.25 = 1.181453906 Reorder the terms: -0.25 + t = 1.181453906 Solving -0.25 + t = 1.181453906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.181453906 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.181453906 + 0.25 t = 1.181453906 + 0.25 Combine like terms: 1.181453906 + 0.25 = 1.431453906 t = 1.431453906 Simplifying t = 1.431453906Subproblem 2
t + -0.25 = -1.181453906 Simplifying t + -0.25 = -1.181453906 Reorder the terms: -0.25 + t = -1.181453906 Solving -0.25 + t = -1.181453906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.181453906 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.181453906 + 0.25 t = -1.181453906 + 0.25 Combine like terms: -1.181453906 + 0.25 = -0.931453906 t = -0.931453906 Simplifying t = -0.931453906Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.431453906, -0.931453906}
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