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Simplifying -4.9t2 + 27.5t + 8.2 = 0 Reorder the terms: 8.2 + 27.5t + -4.9t2 = 0 Solving 8.2 + 27.5t + -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'. -1.673469388 + -5.612244898t + t2 = 0 Move the constant term to the right: Add '1.673469388' to each side of the equation. -1.673469388 + -5.612244898t + 1.673469388 + t2 = 0 + 1.673469388 Reorder the terms: -1.673469388 + 1.673469388 + -5.612244898t + t2 = 0 + 1.673469388 Combine like terms: -1.673469388 + 1.673469388 = 0.000000000 0.000000000 + -5.612244898t + t2 = 0 + 1.673469388 -5.612244898t + t2 = 0 + 1.673469388 Combine like terms: 0 + 1.673469388 = 1.673469388 -5.612244898t + t2 = 1.673469388 The t term is -5.612244898t. Take half its coefficient (-2.806122449). Square it (7.874323199) and add it to both sides. Add '7.874323199' to each side of the equation. -5.612244898t + 7.874323199 + t2 = 1.673469388 + 7.874323199 Reorder the terms: 7.874323199 + -5.612244898t + t2 = 1.673469388 + 7.874323199 Combine like terms: 1.673469388 + 7.874323199 = 9.547792587 7.874323199 + -5.612244898t + t2 = 9.547792587 Factor a perfect square on the left side: (t + -2.806122449)(t + -2.806122449) = 9.547792587 Calculate the square root of the right side: 3.089950256 Break this problem into two subproblems by setting (t + -2.806122449) equal to 3.089950256 and -3.089950256.Subproblem 1
t + -2.806122449 = 3.089950256 Simplifying t + -2.806122449 = 3.089950256 Reorder the terms: -2.806122449 + t = 3.089950256 Solving -2.806122449 + t = 3.089950256 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.806122449' to each side of the equation. -2.806122449 + 2.806122449 + t = 3.089950256 + 2.806122449 Combine like terms: -2.806122449 + 2.806122449 = 0.000000000 0.000000000 + t = 3.089950256 + 2.806122449 t = 3.089950256 + 2.806122449 Combine like terms: 3.089950256 + 2.806122449 = 5.896072705 t = 5.896072705 Simplifying t = 5.896072705Subproblem 2
t + -2.806122449 = -3.089950256 Simplifying t + -2.806122449 = -3.089950256 Reorder the terms: -2.806122449 + t = -3.089950256 Solving -2.806122449 + t = -3.089950256 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.806122449' to each side of the equation. -2.806122449 + 2.806122449 + t = -3.089950256 + 2.806122449 Combine like terms: -2.806122449 + 2.806122449 = 0.000000000 0.000000000 + t = -3.089950256 + 2.806122449 t = -3.089950256 + 2.806122449 Combine like terms: -3.089950256 + 2.806122449 = -0.283827807 t = -0.283827807 Simplifying t = -0.283827807Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.896072705, -0.283827807}
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