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Simplifying -120 = -2(t) + 0.5(-9.8) * t2 Multiply 0.5 * -9.8 -120 = -2t + -4.9t2 Solving -120 = -2t + -4.9t2 Solving for variable 't'. Reorder the terms: -120 + 2t + 4.9t2 = -2t + 2t + -4.9t2 + 4.9t2 Combine like terms: -2t + 2t = 0 -120 + 2t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -120 + 2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -120 + 2t + 4.9t2 = 0.0 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 = 4.7488412653 t = 4.7488412653 Simplifying t = 4.7488412653Subproblem 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 = -5.1570045307 t = -5.1570045307 Simplifying t = -5.1570045307Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.7488412653, -5.1570045307}
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