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Simplifying 4.9t2 + 2.0t + -50.0 = 0 Reorder the terms: -50.0 + 2.0t + 4.9t2 = 0 Solving -50.0 + 2.0t + 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'. -10.20408163 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.4081632653t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.4081632653t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.4081632653t + t2 = 0 + 10.20408163 0.4081632653t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.4081632653t + t2 = 10.20408163 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 = 10.20408163 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 10.20408163 + 0.04164931281 Combine like terms: 10.20408163 + 0.04164931281 = 10.24573094281 0.04164931281 + 0.4081632653t + t2 = 10.24573094281 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 10.24573094281 Calculate the square root of the right side: 3.200895335 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 3.200895335 and -3.200895335.Subproblem 1
t + 0.2040816327 = 3.200895335 Simplifying t + 0.2040816327 = 3.200895335 Reorder the terms: 0.2040816327 + t = 3.200895335 Solving 0.2040816327 + t = 3.200895335 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 = 3.200895335 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 3.200895335 + -0.2040816327 t = 3.200895335 + -0.2040816327 Combine like terms: 3.200895335 + -0.2040816327 = 2.9968137023 t = 2.9968137023 Simplifying t = 2.9968137023Subproblem 2
t + 0.2040816327 = -3.200895335 Simplifying t + 0.2040816327 = -3.200895335 Reorder the terms: 0.2040816327 + t = -3.200895335 Solving 0.2040816327 + t = -3.200895335 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 = -3.200895335 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -3.200895335 + -0.2040816327 t = -3.200895335 + -0.2040816327 Combine like terms: -3.200895335 + -0.2040816327 = -3.4049769677 t = -3.4049769677 Simplifying t = -3.4049769677Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.9968137023, -3.4049769677}
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