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Simplifying 4.9t2 + 0.2t + -0.775 = 0 Reorder the terms: -0.775 + 0.2t + 4.9t2 = 0 Solving -0.775 + 0.2t + 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'. -0.1581632653 + 0.04081632653t + t2 = 0 Move the constant term to the right: Add '0.1581632653' to each side of the equation. -0.1581632653 + 0.04081632653t + 0.1581632653 + t2 = 0 + 0.1581632653 Reorder the terms: -0.1581632653 + 0.1581632653 + 0.04081632653t + t2 = 0 + 0.1581632653 Combine like terms: -0.1581632653 + 0.1581632653 = 0.0000000000 0.0000000000 + 0.04081632653t + t2 = 0 + 0.1581632653 0.04081632653t + t2 = 0 + 0.1581632653 Combine like terms: 0 + 0.1581632653 = 0.1581632653 0.04081632653t + t2 = 0.1581632653 The t term is 0.04081632653t. Take half its coefficient (0.02040816327). Square it (0.0004164931281) and add it to both sides. Add '0.0004164931281' to each side of the equation. 0.04081632653t + 0.0004164931281 + t2 = 0.1581632653 + 0.0004164931281 Reorder the terms: 0.0004164931281 + 0.04081632653t + t2 = 0.1581632653 + 0.0004164931281 Combine like terms: 0.1581632653 + 0.0004164931281 = 0.1585797584281 0.0004164931281 + 0.04081632653t + t2 = 0.1585797584281 Factor a perfect square on the left side: (t + 0.02040816327)(t + 0.02040816327) = 0.1585797584281 Calculate the square root of the right side: 0.398220741 Break this problem into two subproblems by setting (t + 0.02040816327) equal to 0.398220741 and -0.398220741.Subproblem 1
t + 0.02040816327 = 0.398220741 Simplifying t + 0.02040816327 = 0.398220741 Reorder the terms: 0.02040816327 + t = 0.398220741 Solving 0.02040816327 + t = 0.398220741 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.02040816327 + t = 0.398220741 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + t = 0.398220741 + -0.02040816327 t = 0.398220741 + -0.02040816327 Combine like terms: 0.398220741 + -0.02040816327 = 0.37781257773 t = 0.37781257773 Simplifying t = 0.37781257773Subproblem 2
t + 0.02040816327 = -0.398220741 Simplifying t + 0.02040816327 = -0.398220741 Reorder the terms: 0.02040816327 + t = -0.398220741 Solving 0.02040816327 + t = -0.398220741 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.02040816327 + t = -0.398220741 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + t = -0.398220741 + -0.02040816327 t = -0.398220741 + -0.02040816327 Combine like terms: -0.398220741 + -0.02040816327 = -0.41862890427 t = -0.41862890427 Simplifying t = -0.41862890427Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.37781257773, -0.41862890427}
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