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Simplifying -4.9t2 + 27.5t + 8.1 = 0 Reorder the terms: 8.1 + 27.5t + -4.9t2 = 0 Solving 8.1 + 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'. -1.653061224 + -5.612244898t + t2 = 0 Move the constant term to the right: Add '1.653061224' to each side of the equation. -1.653061224 + -5.612244898t + 1.653061224 + t2 = 0 + 1.653061224 Reorder the terms: -1.653061224 + 1.653061224 + -5.612244898t + t2 = 0 + 1.653061224 Combine like terms: -1.653061224 + 1.653061224 = 0.000000000 0.000000000 + -5.612244898t + t2 = 0 + 1.653061224 -5.612244898t + t2 = 0 + 1.653061224 Combine like terms: 0 + 1.653061224 = 1.653061224 -5.612244898t + t2 = 1.653061224 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 = 1.653061224 + 7.874323199 Reorder the terms: 7.874323199 + -5.612244898t + t2 = 1.653061224 + 7.874323199 Combine like terms: 1.653061224 + 7.874323199 = 9.527384423 7.874323199 + -5.612244898t + t2 = 9.527384423 Factor a perfect square on the left side: (t + -2.806122449)(t + -2.806122449) = 9.527384423 Calculate the square root of the right side: 3.086646145 Break this problem into two subproblems by setting (t + -2.806122449) equal to 3.086646145 and -3.086646145.Subproblem 1
t + -2.806122449 = 3.086646145 Simplifying t + -2.806122449 = 3.086646145 Reorder the terms: -2.806122449 + t = 3.086646145 Solving -2.806122449 + t = 3.086646145 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 = 3.086646145 + 2.806122449 Combine like terms: -2.806122449 + 2.806122449 = 0.000000000 0.000000000 + t = 3.086646145 + 2.806122449 t = 3.086646145 + 2.806122449 Combine like terms: 3.086646145 + 2.806122449 = 5.892768594 t = 5.892768594 Simplifying t = 5.892768594Subproblem 2
t + -2.806122449 = -3.086646145 Simplifying t + -2.806122449 = -3.086646145 Reorder the terms: -2.806122449 + t = -3.086646145 Solving -2.806122449 + t = -3.086646145 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 = -3.086646145 + 2.806122449 Combine like terms: -2.806122449 + 2.806122449 = 0.000000000 0.000000000 + t = -3.086646145 + 2.806122449 t = -3.086646145 + 2.806122449 Combine like terms: -3.086646145 + 2.806122449 = -0.280523696 t = -0.280523696 Simplifying t = -0.280523696Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.892768594, -0.280523696}
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