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Simplifying (2t2 + -19t + -18) + -1(-8t2 + 12t + -12) = 0 Reorder the terms: (-18 + -19t + 2t2) + -1(-8t2 + 12t + -12) = 0 Remove parenthesis around (-18 + -19t + 2t2) -18 + -19t + 2t2 + -1(-8t2 + 12t + -12) = 0 Reorder the terms: -18 + -19t + 2t2 + -1(-12 + 12t + -8t2) = 0 -18 + -19t + 2t2 + (-12 * -1 + 12t * -1 + -8t2 * -1) = 0 -18 + -19t + 2t2 + (12 + -12t + 8t2) = 0 Reorder the terms: -18 + 12 + -19t + -12t + 2t2 + 8t2 = 0 Combine like terms: -18 + 12 = -6 -6 + -19t + -12t + 2t2 + 8t2 = 0 Combine like terms: -19t + -12t = -31t -6 + -31t + 2t2 + 8t2 = 0 Combine like terms: 2t2 + 8t2 = 10t2 -6 + -31t + 10t2 = 0 Solving -6 + -31t + 10t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -3.1t + t2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.1t + 0.6 + t2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.1t + t2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.1t + t2 = 0.0 + 0.6 -3.1t + t2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -3.1t + t2 = 0.6 The t term is -3.1t. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1t + 2.4025 + t2 = 0.6 + 2.4025 Reorder the terms: 2.4025 + -3.1t + t2 = 0.6 + 2.4025 Combine like terms: 0.6 + 2.4025 = 3.0025 2.4025 + -3.1t + t2 = 3.0025 Factor a perfect square on the left side: (t + -1.55)(t + -1.55) = 3.0025 Calculate the square root of the right side: 1.732772345 Break this problem into two subproblems by setting (t + -1.55) equal to 1.732772345 and -1.732772345.Subproblem 1
t + -1.55 = 1.732772345 Simplifying t + -1.55 = 1.732772345 Reorder the terms: -1.55 + t = 1.732772345 Solving -1.55 + t = 1.732772345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + t = 1.732772345 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + t = 1.732772345 + 1.55 t = 1.732772345 + 1.55 Combine like terms: 1.732772345 + 1.55 = 3.282772345 t = 3.282772345 Simplifying t = 3.282772345Subproblem 2
t + -1.55 = -1.732772345 Simplifying t + -1.55 = -1.732772345 Reorder the terms: -1.55 + t = -1.732772345 Solving -1.55 + t = -1.732772345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + t = -1.732772345 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + t = -1.732772345 + 1.55 t = -1.732772345 + 1.55 Combine like terms: -1.732772345 + 1.55 = -0.182772345 t = -0.182772345 Simplifying t = -0.182772345Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.282772345, -0.182772345}
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