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Simplifying -4.9t2 + 2t + 450 = 0 Reorder the terms: 450 + 2t + -4.9t2 = 0 Solving 450 + 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'. -91.83673469 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '91.83673469' to each side of the equation. -91.83673469 + -0.4081632653t + 91.83673469 + t2 = 0 + 91.83673469 Reorder the terms: -91.83673469 + 91.83673469 + -0.4081632653t + t2 = 0 + 91.83673469 Combine like terms: -91.83673469 + 91.83673469 = 0.00000000 0.00000000 + -0.4081632653t + t2 = 0 + 91.83673469 -0.4081632653t + t2 = 0 + 91.83673469 Combine like terms: 0 + 91.83673469 = 91.83673469 -0.4081632653t + t2 = 91.83673469 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 = 91.83673469 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 91.83673469 + 0.04164931281 Combine like terms: 91.83673469 + 0.04164931281 = 91.87838400281 0.04164931281 + -0.4081632653t + t2 = 91.87838400281 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 91.87838400281 Calculate the square root of the right side: 9.585321278 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 9.585321278 and -9.585321278.Subproblem 1
t + -0.2040816327 = 9.585321278 Simplifying t + -0.2040816327 = 9.585321278 Reorder the terms: -0.2040816327 + t = 9.585321278 Solving -0.2040816327 + t = 9.585321278 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 = 9.585321278 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 9.585321278 + 0.2040816327 t = 9.585321278 + 0.2040816327 Combine like terms: 9.585321278 + 0.2040816327 = 9.7894029107 t = 9.7894029107 Simplifying t = 9.7894029107Subproblem 2
t + -0.2040816327 = -9.585321278 Simplifying t + -0.2040816327 = -9.585321278 Reorder the terms: -0.2040816327 + t = -9.585321278 Solving -0.2040816327 + t = -9.585321278 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 = -9.585321278 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -9.585321278 + 0.2040816327 t = -9.585321278 + 0.2040816327 Combine like terms: -9.585321278 + 0.2040816327 = -9.3812396453 t = -9.3812396453 Simplifying t = -9.3812396453Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.7894029107, -9.3812396453}
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