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Simplifying 5t2 + -11t + -96 = 0 Reorder the terms: -96 + -11t + 5t2 = 0 Solving -96 + -11t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + -2.2t + t2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -2.2t + 19.2 + t2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -2.2t + t2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -2.2t + t2 = 0 + 19.2 -2.2t + t2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -2.2t + t2 = 19.2 The t term is -2.2t. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2t + 1.21 + t2 = 19.2 + 1.21 Reorder the terms: 1.21 + -2.2t + t2 = 19.2 + 1.21 Combine like terms: 19.2 + 1.21 = 20.41 1.21 + -2.2t + t2 = 20.41 Factor a perfect square on the left side: (t + -1.1)(t + -1.1) = 20.41 Calculate the square root of the right side: 4.517742799 Break this problem into two subproblems by setting (t + -1.1) equal to 4.517742799 and -4.517742799.Subproblem 1
t + -1.1 = 4.517742799 Simplifying t + -1.1 = 4.517742799 Reorder the terms: -1.1 + t = 4.517742799 Solving -1.1 + t = 4.517742799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = 4.517742799 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = 4.517742799 + 1.1 t = 4.517742799 + 1.1 Combine like terms: 4.517742799 + 1.1 = 5.617742799 t = 5.617742799 Simplifying t = 5.617742799Subproblem 2
t + -1.1 = -4.517742799 Simplifying t + -1.1 = -4.517742799 Reorder the terms: -1.1 + t = -4.517742799 Solving -1.1 + t = -4.517742799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = -4.517742799 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = -4.517742799 + 1.1 t = -4.517742799 + 1.1 Combine like terms: -4.517742799 + 1.1 = -3.417742799 t = -3.417742799 Simplifying t = -3.417742799Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.617742799, -3.417742799}
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