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Simplifying 0.0765t2 + -0.894t + 1.885 = 0 Reorder the terms: 1.885 + -0.894t + 0.0765t2 = 0 Solving 1.885 + -0.894t + 0.0765t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0765 the coefficient of the squared term: Divide each side by '0.0765'. 24.64052288 + -11.68627451t + t2 = 0 Move the constant term to the right: Add '-24.64052288' to each side of the equation. 24.64052288 + -11.68627451t + -24.64052288 + t2 = 0 + -24.64052288 Reorder the terms: 24.64052288 + -24.64052288 + -11.68627451t + t2 = 0 + -24.64052288 Combine like terms: 24.64052288 + -24.64052288 = 0.00000000 0.00000000 + -11.68627451t + t2 = 0 + -24.64052288 -11.68627451t + t2 = 0 + -24.64052288 Combine like terms: 0 + -24.64052288 = -24.64052288 -11.68627451t + t2 = -24.64052288 The t term is -11.68627451t. Take half its coefficient (-5.843137255). Square it (34.14225298) and add it to both sides. Add '34.14225298' to each side of the equation. -11.68627451t + 34.14225298 + t2 = -24.64052288 + 34.14225298 Reorder the terms: 34.14225298 + -11.68627451t + t2 = -24.64052288 + 34.14225298 Combine like terms: -24.64052288 + 34.14225298 = 9.5017301 34.14225298 + -11.68627451t + t2 = 9.5017301 Factor a perfect square on the left side: (t + -5.843137255)(t + -5.843137255) = 9.5017301 Calculate the square root of the right side: 3.082487648 Break this problem into two subproblems by setting (t + -5.843137255) equal to 3.082487648 and -3.082487648.Subproblem 1
t + -5.843137255 = 3.082487648 Simplifying t + -5.843137255 = 3.082487648 Reorder the terms: -5.843137255 + t = 3.082487648 Solving -5.843137255 + t = 3.082487648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.843137255' to each side of the equation. -5.843137255 + 5.843137255 + t = 3.082487648 + 5.843137255 Combine like terms: -5.843137255 + 5.843137255 = 0.000000000 0.000000000 + t = 3.082487648 + 5.843137255 t = 3.082487648 + 5.843137255 Combine like terms: 3.082487648 + 5.843137255 = 8.925624903 t = 8.925624903 Simplifying t = 8.925624903Subproblem 2
t + -5.843137255 = -3.082487648 Simplifying t + -5.843137255 = -3.082487648 Reorder the terms: -5.843137255 + t = -3.082487648 Solving -5.843137255 + t = -3.082487648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.843137255' to each side of the equation. -5.843137255 + 5.843137255 + t = -3.082487648 + 5.843137255 Combine like terms: -5.843137255 + 5.843137255 = 0.000000000 0.000000000 + t = -3.082487648 + 5.843137255 t = -3.082487648 + 5.843137255 Combine like terms: -3.082487648 + 5.843137255 = 2.760649607 t = 2.760649607 Simplifying t = 2.760649607Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.925624903, 2.760649607}
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