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Simplifying -4.9t2 + 26t + 20 = 0 Reorder the terms: 20 + 26t + -4.9t2 = 0 Solving 20 + 26t + -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 + -5.306122449t + t2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -5.306122449t + 4.081632653 + t2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -5.306122449t + t2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -5.306122449t + t2 = 0 + 4.081632653 -5.306122449t + t2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -5.306122449t + t2 = 4.081632653 The t term is -5.306122449t. Take half its coefficient (-2.653061225). Square it (7.038733864) and add it to both sides. Add '7.038733864' to each side of the equation. -5.306122449t + 7.038733864 + t2 = 4.081632653 + 7.038733864 Reorder the terms: 7.038733864 + -5.306122449t + t2 = 4.081632653 + 7.038733864 Combine like terms: 4.081632653 + 7.038733864 = 11.120366517 7.038733864 + -5.306122449t + t2 = 11.120366517 Factor a perfect square on the left side: (t + -2.653061225)(t + -2.653061225) = 11.120366517 Calculate the square root of the right side: 3.334721355 Break this problem into two subproblems by setting (t + -2.653061225) equal to 3.334721355 and -3.334721355.Subproblem 1
t + -2.653061225 = 3.334721355 Simplifying t + -2.653061225 = 3.334721355 Reorder the terms: -2.653061225 + t = 3.334721355 Solving -2.653061225 + t = 3.334721355 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = 3.334721355 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = 3.334721355 + 2.653061225 t = 3.334721355 + 2.653061225 Combine like terms: 3.334721355 + 2.653061225 = 5.98778258 t = 5.98778258 Simplifying t = 5.98778258Subproblem 2
t + -2.653061225 = -3.334721355 Simplifying t + -2.653061225 = -3.334721355 Reorder the terms: -2.653061225 + t = -3.334721355 Solving -2.653061225 + t = -3.334721355 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.653061225' to each side of the equation. -2.653061225 + 2.653061225 + t = -3.334721355 + 2.653061225 Combine like terms: -2.653061225 + 2.653061225 = 0.000000000 0.000000000 + t = -3.334721355 + 2.653061225 t = -3.334721355 + 2.653061225 Combine like terms: -3.334721355 + 2.653061225 = -0.68166013 t = -0.68166013 Simplifying t = -0.68166013Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.98778258, -0.68166013}
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