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Simplifying 3 + 23.5t + -4.9t2 = 0 Solving 3 + 23.5t + -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'. -0.612244898 + -4.795918367t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -4.795918367t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -4.795918367t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -4.795918367t + t2 = 0 + 0.612244898 -4.795918367t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -4.795918367t + t2 = 0.612244898 The t term is -4.795918367t. Take half its coefficient (-2.397959184). Square it (5.750208248) and add it to both sides. Add '5.750208248' to each side of the equation. -4.795918367t + 5.750208248 + t2 = 0.612244898 + 5.750208248 Reorder the terms: 5.750208248 + -4.795918367t + t2 = 0.612244898 + 5.750208248 Combine like terms: 0.612244898 + 5.750208248 = 6.362453146 5.750208248 + -4.795918367t + t2 = 6.362453146 Factor a perfect square on the left side: (t + -2.397959184)(t + -2.397959184) = 6.362453146 Calculate the square root of the right side: 2.522390364 Break this problem into two subproblems by setting (t + -2.397959184) equal to 2.522390364 and -2.522390364.Subproblem 1
t + -2.397959184 = 2.522390364 Simplifying t + -2.397959184 = 2.522390364 Reorder the terms: -2.397959184 + t = 2.522390364 Solving -2.397959184 + t = 2.522390364 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = 2.522390364 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = 2.522390364 + 2.397959184 t = 2.522390364 + 2.397959184 Combine like terms: 2.522390364 + 2.397959184 = 4.920349548 t = 4.920349548 Simplifying t = 4.920349548Subproblem 2
t + -2.397959184 = -2.522390364 Simplifying t + -2.397959184 = -2.522390364 Reorder the terms: -2.397959184 + t = -2.522390364 Solving -2.397959184 + t = -2.522390364 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = -2.522390364 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = -2.522390364 + 2.397959184 t = -2.522390364 + 2.397959184 Combine like terms: -2.522390364 + 2.397959184 = -0.12443118 t = -0.12443118 Simplifying t = -0.12443118Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.920349548, -0.12443118}
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