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Simplifying -4.9t2 + 20t + 240 = 0 Reorder the terms: 240 + 20t + -4.9t2 = 0 Solving 240 + 20t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -48.97959184 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '48.97959184' to each side of the equation. -48.97959184 + -4.081632653t + 48.97959184 + t2 = 0 + 48.97959184 Reorder the terms: -48.97959184 + 48.97959184 + -4.081632653t + t2 = 0 + 48.97959184 Combine like terms: -48.97959184 + 48.97959184 = 0.00000000 0.00000000 + -4.081632653t + t2 = 0 + 48.97959184 -4.081632653t + t2 = 0 + 48.97959184 Combine like terms: 0 + 48.97959184 = 48.97959184 -4.081632653t + t2 = 48.97959184 The t term is -4.081632653t. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653t + 4.164931281 + t2 = 48.97959184 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 48.97959184 + 4.164931281 Combine like terms: 48.97959184 + 4.164931281 = 53.144523121 4.164931281 + -4.081632653t + t2 = 53.144523121 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 53.144523121 Calculate the square root of the right side: 7.290029021 Break this problem into two subproblems by setting (t + -2.040816327) equal to 7.290029021 and -7.290029021.Subproblem 1
t + -2.040816327 = 7.290029021 Simplifying t + -2.040816327 = 7.290029021 Reorder the terms: -2.040816327 + t = 7.290029021 Solving -2.040816327 + t = 7.290029021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = 7.290029021 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 7.290029021 + 2.040816327 t = 7.290029021 + 2.040816327 Combine like terms: 7.290029021 + 2.040816327 = 9.330845348 t = 9.330845348 Simplifying t = 9.330845348Subproblem 2
t + -2.040816327 = -7.290029021 Simplifying t + -2.040816327 = -7.290029021 Reorder the terms: -2.040816327 + t = -7.290029021 Solving -2.040816327 + t = -7.290029021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = -7.290029021 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -7.290029021 + 2.040816327 t = -7.290029021 + 2.040816327 Combine like terms: -7.290029021 + 2.040816327 = -5.249212694 t = -5.249212694 Simplifying t = -5.249212694Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.330845348, -5.249212694}
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