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Simplifying 4.9t2 + 2t + -45 = 0 Reorder the terms: -45 + 2t + 4.9t2 = 0 Solving -45 + 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'. -9.183673469 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + 0.4081632653t + 9.183673469 + t2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + 0.4081632653t + t2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + 0.4081632653t + t2 = 0 + 9.183673469 0.4081632653t + t2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 0.4081632653t + t2 = 9.183673469 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 = 9.183673469 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 9.183673469 + 0.04164931281 Combine like terms: 9.183673469 + 0.04164931281 = 9.22532278181 0.04164931281 + 0.4081632653t + t2 = 9.22532278181 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 9.22532278181 Calculate the square root of the right side: 3.037321646 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 3.037321646 and -3.037321646.Subproblem 1
t + 0.2040816327 = 3.037321646 Simplifying t + 0.2040816327 = 3.037321646 Reorder the terms: 0.2040816327 + t = 3.037321646 Solving 0.2040816327 + t = 3.037321646 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 = 3.037321646 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 3.037321646 + -0.2040816327 t = 3.037321646 + -0.2040816327 Combine like terms: 3.037321646 + -0.2040816327 = 2.8332400133 t = 2.8332400133 Simplifying t = 2.8332400133Subproblem 2
t + 0.2040816327 = -3.037321646 Simplifying t + 0.2040816327 = -3.037321646 Reorder the terms: 0.2040816327 + t = -3.037321646 Solving 0.2040816327 + t = -3.037321646 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 = -3.037321646 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -3.037321646 + -0.2040816327 t = -3.037321646 + -0.2040816327 Combine like terms: -3.037321646 + -0.2040816327 = -3.2414032787 t = -3.2414032787 Simplifying t = -3.2414032787Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.8332400133, -3.2414032787}
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