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Simplifying 4.9t2 + 20t + 20 = 0 Reorder the terms: 20 + 20t + 4.9t2 = 0 Solving 20 + 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'. 4.081632653 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '-4.081632653' to each side of the equation. 4.081632653 + 4.081632653t + -4.081632653 + t2 = 0 + -4.081632653 Reorder the terms: 4.081632653 + -4.081632653 + 4.081632653t + t2 = 0 + -4.081632653 Combine like terms: 4.081632653 + -4.081632653 = 0.000000000 0.000000000 + 4.081632653t + t2 = 0 + -4.081632653 4.081632653t + t2 = 0 + -4.081632653 Combine like terms: 0 + -4.081632653 = -4.081632653 4.081632653t + t2 = -4.081632653 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 = -4.081632653 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = -4.081632653 + 4.164931281 Combine like terms: -4.081632653 + 4.164931281 = 0.083298628 4.164931281 + 4.081632653t + t2 = 0.083298628 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 0.083298628 Calculate the square root of the right side: 0.288615017 Break this problem into two subproblems by setting (t + 2.040816327) equal to 0.288615017 and -0.288615017.Subproblem 1
t + 2.040816327 = 0.288615017 Simplifying t + 2.040816327 = 0.288615017 Reorder the terms: 2.040816327 + t = 0.288615017 Solving 2.040816327 + t = 0.288615017 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 = 0.288615017 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 0.288615017 + -2.040816327 t = 0.288615017 + -2.040816327 Combine like terms: 0.288615017 + -2.040816327 = -1.75220131 t = -1.75220131 Simplifying t = -1.75220131Subproblem 2
t + 2.040816327 = -0.288615017 Simplifying t + 2.040816327 = -0.288615017 Reorder the terms: 2.040816327 + t = -0.288615017 Solving 2.040816327 + t = -0.288615017 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 = -0.288615017 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -0.288615017 + -2.040816327 t = -0.288615017 + -2.040816327 Combine like terms: -0.288615017 + -2.040816327 = -2.329431344 t = -2.329431344 Simplifying t = -2.329431344Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.75220131, -2.329431344}
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