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Simplifying -4.9t2 + -2t + 49 = 0 Reorder the terms: 49 + -2t + -4.9t2 = 0 Solving 49 + -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'. -10 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.4081632653t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + 0.4081632653t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.4081632653t + t2 = 0 + 10 0.4081632653t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.4081632653t + t2 = 10 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 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 10 + 0.04164931281 Combine like terms: 10 + 0.04164931281 = 10.04164931281 0.04164931281 + 0.4081632653t + t2 = 10.04164931281 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 10.04164931281 Calculate the square root of the right side: 3.168856152 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 3.168856152 and -3.168856152.Subproblem 1
t + 0.2040816327 = 3.168856152 Simplifying t + 0.2040816327 = 3.168856152 Reorder the terms: 0.2040816327 + t = 3.168856152 Solving 0.2040816327 + t = 3.168856152 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 = 3.168856152 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 3.168856152 + -0.2040816327 t = 3.168856152 + -0.2040816327 Combine like terms: 3.168856152 + -0.2040816327 = 2.9647745193 t = 2.9647745193 Simplifying t = 2.9647745193Subproblem 2
t + 0.2040816327 = -3.168856152 Simplifying t + 0.2040816327 = -3.168856152 Reorder the terms: 0.2040816327 + t = -3.168856152 Solving 0.2040816327 + t = -3.168856152 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 = -3.168856152 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -3.168856152 + -0.2040816327 t = -3.168856152 + -0.2040816327 Combine like terms: -3.168856152 + -0.2040816327 = -3.3729377847 t = -3.3729377847 Simplifying t = -3.3729377847Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.9647745193, -3.3729377847}
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