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Simplifying 0 = 4.9t2 + 2t + -100 Reorder the terms: 0 = -100 + 2t + 4.9t2 Solving 0 = -100 + 2t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 100 = 100 100 + -2t + -4.9t2 = -100 + 2t + 4.9t2 + 100 + -2t + -4.9t2 Reorder the terms: 100 + -2t + -4.9t2 = -100 + 100 + 2t + -2t + 4.9t2 + -4.9t2 Combine like terms: -100 + 100 = 0 100 + -2t + -4.9t2 = 0 + 2t + -2t + 4.9t2 + -4.9t2 100 + -2t + -4.9t2 = 2t + -2t + 4.9t2 + -4.9t2 Combine like terms: 2t + -2t = 0 100 + -2t + -4.9t2 = 0 + 4.9t2 + -4.9t2 100 + -2t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 100 + -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'. -20.40816327 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + 0.4081632653t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + 0.4081632653t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + 0.4081632653t + t2 = 0 + 20.40816327 0.4081632653t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 0.4081632653t + t2 = 20.40816327 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 = 20.40816327 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 20.40816327 + 0.04164931281 Combine like terms: 20.40816327 + 0.04164931281 = 20.44981258281 0.04164931281 + 0.4081632653t + t2 = 20.44981258281 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 20.44981258281 Calculate the square root of the right side: 4.5221469 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 4.5221469 and -4.5221469.Subproblem 1
t + 0.2040816327 = 4.5221469 Simplifying t + 0.2040816327 = 4.5221469 Reorder the terms: 0.2040816327 + t = 4.5221469 Solving 0.2040816327 + t = 4.5221469 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 = 4.5221469 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 4.5221469 + -0.2040816327 t = 4.5221469 + -0.2040816327 Combine like terms: 4.5221469 + -0.2040816327 = 4.3180652673 t = 4.3180652673 Simplifying t = 4.3180652673Subproblem 2
t + 0.2040816327 = -4.5221469 Simplifying t + 0.2040816327 = -4.5221469 Reorder the terms: 0.2040816327 + t = -4.5221469 Solving 0.2040816327 + t = -4.5221469 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 = -4.5221469 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -4.5221469 + -0.2040816327 t = -4.5221469 + -0.2040816327 Combine like terms: -4.5221469 + -0.2040816327 = -4.7262285327 t = -4.7262285327 Simplifying t = -4.7262285327Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.3180652673, -4.7262285327}
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