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Simplifying 4.9t2 + 2t + -20 = 0 Reorder the terms: -20 + 2t + 4.9t2 = 0 Solving -20 + 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'. -4.081632653 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 0.4081632653t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 0.4081632653t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 0.4081632653t + t2 = 0 + 4.081632653 0.4081632653t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 0.4081632653t + t2 = 4.081632653 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 = 4.081632653 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 4.081632653 + 0.04164931281 Combine like terms: 4.081632653 + 0.04164931281 = 4.12328196581 0.04164931281 + 0.4081632653t + t2 = 4.12328196581 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 4.12328196581 Calculate the square root of the right side: 2.030586606 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 2.030586606 and -2.030586606.Subproblem 1
t + 0.2040816327 = 2.030586606 Simplifying t + 0.2040816327 = 2.030586606 Reorder the terms: 0.2040816327 + t = 2.030586606 Solving 0.2040816327 + t = 2.030586606 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 = 2.030586606 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 2.030586606 + -0.2040816327 t = 2.030586606 + -0.2040816327 Combine like terms: 2.030586606 + -0.2040816327 = 1.8265049733 t = 1.8265049733 Simplifying t = 1.8265049733Subproblem 2
t + 0.2040816327 = -2.030586606 Simplifying t + 0.2040816327 = -2.030586606 Reorder the terms: 0.2040816327 + t = -2.030586606 Solving 0.2040816327 + t = -2.030586606 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 = -2.030586606 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -2.030586606 + -0.2040816327 t = -2.030586606 + -0.2040816327 Combine like terms: -2.030586606 + -0.2040816327 = -2.2346682387 t = -2.2346682387 Simplifying t = -2.2346682387Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8265049733, -2.2346682387}
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