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Simplifying 4.9t2 + -14t + -52 = 0 Reorder the terms: -52 + -14t + 4.9t2 = 0 Solving -52 + -14t + 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'. -10.6122449 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '10.6122449' to each side of the equation. -10.6122449 + -2.857142857t + 10.6122449 + t2 = 0 + 10.6122449 Reorder the terms: -10.6122449 + 10.6122449 + -2.857142857t + t2 = 0 + 10.6122449 Combine like terms: -10.6122449 + 10.6122449 = 0.0000000 0.0000000 + -2.857142857t + t2 = 0 + 10.6122449 -2.857142857t + t2 = 0 + 10.6122449 Combine like terms: 0 + 10.6122449 = 10.6122449 -2.857142857t + t2 = 10.6122449 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = 10.6122449 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 10.6122449 + 2.040816328 Combine like terms: 10.6122449 + 2.040816328 = 12.653061228 2.040816328 + -2.857142857t + t2 = 12.653061228 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 12.653061228 Calculate the square root of the right side: 3.557114171 Break this problem into two subproblems by setting (t + -1.428571429) equal to 3.557114171 and -3.557114171.Subproblem 1
t + -1.428571429 = 3.557114171 Simplifying t + -1.428571429 = 3.557114171 Reorder the terms: -1.428571429 + t = 3.557114171 Solving -1.428571429 + t = 3.557114171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 3.557114171 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 3.557114171 + 1.428571429 t = 3.557114171 + 1.428571429 Combine like terms: 3.557114171 + 1.428571429 = 4.9856856 t = 4.9856856 Simplifying t = 4.9856856Subproblem 2
t + -1.428571429 = -3.557114171 Simplifying t + -1.428571429 = -3.557114171 Reorder the terms: -1.428571429 + t = -3.557114171 Solving -1.428571429 + t = -3.557114171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -3.557114171 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -3.557114171 + 1.428571429 t = -3.557114171 + 1.428571429 Combine like terms: -3.557114171 + 1.428571429 = -2.128542742 t = -2.128542742 Simplifying t = -2.128542742Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.9856856, -2.128542742}
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