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Simplifying 4.9t2 + -2t + -120 = 0 Reorder the terms: -120 + -2t + 4.9t2 = 0 Solving -120 + -2t + 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'. -24.48979592 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + -0.4081632653t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + -0.4081632653t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + -0.4081632653t + t2 = 0 + 24.48979592 -0.4081632653t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 -0.4081632653t + t2 = 24.48979592 The t term is -0.4081632653t. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653t + 0.04164931281 + t2 = 24.48979592 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 24.48979592 + 0.04164931281 Combine like terms: 24.48979592 + 0.04164931281 = 24.53144523281 0.04164931281 + -0.4081632653t + t2 = 24.53144523281 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 24.53144523281 Calculate the square root of the right side: 4.952922898 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 4.952922898 and -4.952922898.Subproblem 1
t + -0.2040816327 = 4.952922898 Simplifying t + -0.2040816327 = 4.952922898 Reorder the terms: -0.2040816327 + t = 4.952922898 Solving -0.2040816327 + t = 4.952922898 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = 4.952922898 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 4.952922898 + 0.2040816327 t = 4.952922898 + 0.2040816327 Combine like terms: 4.952922898 + 0.2040816327 = 5.1570045307 t = 5.1570045307 Simplifying t = 5.1570045307Subproblem 2
t + -0.2040816327 = -4.952922898 Simplifying t + -0.2040816327 = -4.952922898 Reorder the terms: -0.2040816327 + t = -4.952922898 Solving -0.2040816327 + t = -4.952922898 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = -4.952922898 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -4.952922898 + 0.2040816327 t = -4.952922898 + 0.2040816327 Combine like terms: -4.952922898 + 0.2040816327 = -4.7488412653 t = -4.7488412653 Simplifying t = -4.7488412653Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.1570045307, -4.7488412653}
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