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Simplifying 4.9t2 + -20t + -2 = 0 Reorder the terms: -2 + -20t + 4.9t2 = 0 Solving -2 + -20t + 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'. -0.4081632653 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -4.081632653t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -4.081632653t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -4.081632653t + t2 = 0 + 0.4081632653 -4.081632653t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -4.081632653t + t2 = 0.4081632653 The t term is -4.081632653t. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653t + 4.164931281 + t2 = 0.4081632653 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 0.4081632653 + 4.164931281 Combine like terms: 0.4081632653 + 4.164931281 = 4.5730945463 4.164931281 + -4.081632653t + t2 = 4.5730945463 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 4.5730945463 Calculate the square root of the right side: 2.138479494 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.138479494 and -2.138479494.Subproblem 1
t + -2.040816327 = 2.138479494 Simplifying t + -2.040816327 = 2.138479494 Reorder the terms: -2.040816327 + t = 2.138479494 Solving -2.040816327 + t = 2.138479494 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = 2.138479494 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.138479494 + 2.040816327 t = 2.138479494 + 2.040816327 Combine like terms: 2.138479494 + 2.040816327 = 4.179295821 t = 4.179295821 Simplifying t = 4.179295821Subproblem 2
t + -2.040816327 = -2.138479494 Simplifying t + -2.040816327 = -2.138479494 Reorder the terms: -2.040816327 + t = -2.138479494 Solving -2.040816327 + t = -2.138479494 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + t = -2.138479494 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.138479494 + 2.040816327 t = -2.138479494 + 2.040816327 Combine like terms: -2.138479494 + 2.040816327 = -0.097663167 t = -0.097663167 Simplifying t = -0.097663167Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.179295821, -0.097663167}
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