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Simplifying 49t2 + 2t + -20 = 0 Reorder the terms: -20 + 2t + 49t2 = 0 Solving -20 + 2t + 49t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.4081632653 + 0.04081632653t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.04081632653t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 0.04081632653t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 0.04081632653t + t2 = 0 + 0.4081632653 0.04081632653t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 0.04081632653t + t2 = 0.4081632653 The t term is 0.04081632653t. Take half its coefficient (0.02040816327). Square it (0.0004164931281) and add it to both sides. Add '0.0004164931281' to each side of the equation. 0.04081632653t + 0.0004164931281 + t2 = 0.4081632653 + 0.0004164931281 Reorder the terms: 0.0004164931281 + 0.04081632653t + t2 = 0.4081632653 + 0.0004164931281 Combine like terms: 0.4081632653 + 0.0004164931281 = 0.4085797584281 0.0004164931281 + 0.04081632653t + t2 = 0.4085797584281 Factor a perfect square on the left side: (t + 0.02040816327)(t + 0.02040816327) = 0.4085797584281 Calculate the square root of the right side: 0.639202439 Break this problem into two subproblems by setting (t + 0.02040816327) equal to 0.639202439 and -0.639202439.Subproblem 1
t + 0.02040816327 = 0.639202439 Simplifying t + 0.02040816327 = 0.639202439 Reorder the terms: 0.02040816327 + t = 0.639202439 Solving 0.02040816327 + t = 0.639202439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.02040816327 + t = 0.639202439 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + t = 0.639202439 + -0.02040816327 t = 0.639202439 + -0.02040816327 Combine like terms: 0.639202439 + -0.02040816327 = 0.61879427573 t = 0.61879427573 Simplifying t = 0.61879427573Subproblem 2
t + 0.02040816327 = -0.639202439 Simplifying t + 0.02040816327 = -0.639202439 Reorder the terms: 0.02040816327 + t = -0.639202439 Solving 0.02040816327 + t = -0.639202439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.02040816327 + t = -0.639202439 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + t = -0.639202439 + -0.02040816327 t = -0.639202439 + -0.02040816327 Combine like terms: -0.639202439 + -0.02040816327 = -0.65961060227 t = -0.65961060227 Simplifying t = -0.65961060227Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.61879427573, -0.65961060227}
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