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Simplifying -3t(4t + -4) + 8t = 3t + -4 Reorder the terms: -3t(-4 + 4t) + 8t = 3t + -4 (-4 * -3t + 4t * -3t) + 8t = 3t + -4 (12t + -12t2) + 8t = 3t + -4 Reorder the terms: 12t + 8t + -12t2 = 3t + -4 Combine like terms: 12t + 8t = 20t 20t + -12t2 = 3t + -4 Reorder the terms: 20t + -12t2 = -4 + 3t Solving 20t + -12t2 = -4 + 3t Solving for variable 't'. Reorder the terms: 4 + 20t + -3t + -12t2 = -4 + 3t + 4 + -3t Combine like terms: 20t + -3t = 17t 4 + 17t + -12t2 = -4 + 3t + 4 + -3t Reorder the terms: 4 + 17t + -12t2 = -4 + 4 + 3t + -3t Combine like terms: -4 + 4 = 0 4 + 17t + -12t2 = 0 + 3t + -3t 4 + 17t + -12t2 = 3t + -3t Combine like terms: 3t + -3t = 0 4 + 17t + -12t2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.3333333333 + -1.416666667t + t2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.416666667t + 0.3333333333 + t2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.416666667t + t2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.416666667t + t2 = 0 + 0.3333333333 -1.416666667t + t2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.416666667t + t2 = 0.3333333333 The t term is -1.416666667t. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667t + 0.5017361113 + t2 = 0.3333333333 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667t + t2 = 0.3333333333 + 0.5017361113 Combine like terms: 0.3333333333 + 0.5017361113 = 0.8350694446 0.5017361113 + -1.416666667t + t2 = 0.8350694446 Factor a perfect square on the left side: (t + -0.7083333335)(t + -0.7083333335) = 0.8350694446 Calculate the square root of the right side: 0.913821342 Break this problem into two subproblems by setting (t + -0.7083333335) equal to 0.913821342 and -0.913821342.Subproblem 1
t + -0.7083333335 = 0.913821342 Simplifying t + -0.7083333335 = 0.913821342 Reorder the terms: -0.7083333335 + t = 0.913821342 Solving -0.7083333335 + t = 0.913821342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + t = 0.913821342 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + t = 0.913821342 + 0.7083333335 t = 0.913821342 + 0.7083333335 Combine like terms: 0.913821342 + 0.7083333335 = 1.6221546755 t = 1.6221546755 Simplifying t = 1.6221546755Subproblem 2
t + -0.7083333335 = -0.913821342 Simplifying t + -0.7083333335 = -0.913821342 Reorder the terms: -0.7083333335 + t = -0.913821342 Solving -0.7083333335 + t = -0.913821342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + t = -0.913821342 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + t = -0.913821342 + 0.7083333335 t = -0.913821342 + 0.7083333335 Combine like terms: -0.913821342 + 0.7083333335 = -0.2054880085 t = -0.2054880085 Simplifying t = -0.2054880085Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6221546755, -0.2054880085}
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