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Simplifying -4.9t2 + 2t + 4 = 0 Reorder the terms: 4 + 2t + -4.9t2 = 0 Solving 4 + 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'. -0.8163265306 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -0.4081632653t + 0.8163265306 + t2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -0.4081632653t + t2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -0.4081632653t + t2 = 0 + 0.8163265306 -0.4081632653t + t2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -0.4081632653t + t2 = 0.8163265306 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 = 0.8163265306 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 0.8163265306 + 0.04164931281 Combine like terms: 0.8163265306 + 0.04164931281 = 0.85797584341 0.04164931281 + -0.4081632653t + t2 = 0.85797584341 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 0.85797584341 Calculate the square root of the right side: 0.926269855 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 0.926269855 and -0.926269855.Subproblem 1
t + -0.2040816327 = 0.926269855 Simplifying t + -0.2040816327 = 0.926269855 Reorder the terms: -0.2040816327 + t = 0.926269855 Solving -0.2040816327 + t = 0.926269855 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 = 0.926269855 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 0.926269855 + 0.2040816327 t = 0.926269855 + 0.2040816327 Combine like terms: 0.926269855 + 0.2040816327 = 1.1303514877 t = 1.1303514877 Simplifying t = 1.1303514877Subproblem 2
t + -0.2040816327 = -0.926269855 Simplifying t + -0.2040816327 = -0.926269855 Reorder the terms: -0.2040816327 + t = -0.926269855 Solving -0.2040816327 + t = -0.926269855 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 = -0.926269855 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -0.926269855 + 0.2040816327 t = -0.926269855 + 0.2040816327 Combine like terms: -0.926269855 + 0.2040816327 = -0.7221882223 t = -0.7221882223 Simplifying t = -0.7221882223Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1303514877, -0.7221882223}
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