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Simplifying 24 = 2 + 11t + -1t2 Solving 24 = 2 + 11t + -1t2 Solving for variable 't'. Combine like terms: 24 + -2 = 22 22 + -11t + t2 = 2 + 11t + -1t2 + -2 + -11t + t2 Reorder the terms: 22 + -11t + t2 = 2 + -2 + 11t + -11t + -1t2 + t2 Combine like terms: 2 + -2 = 0 22 + -11t + t2 = 0 + 11t + -11t + -1t2 + t2 22 + -11t + t2 = 11t + -11t + -1t2 + t2 Combine like terms: 11t + -11t = 0 22 + -11t + t2 = 0 + -1t2 + t2 22 + -11t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 22 + -11t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -11t + -22 + t2 = 0 + -22 Reorder the terms: 22 + -22 + -11t + t2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -11t + t2 = 0 + -22 -11t + t2 = 0 + -22 Combine like terms: 0 + -22 = -22 -11t + t2 = -22 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -22 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -22 + 30.25 Combine like terms: -22 + 30.25 = 8.25 30.25 + -11t + t2 = 8.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (t + -5.5) equal to 2.872281323 and -2.872281323.Subproblem 1
t + -5.5 = 2.872281323 Simplifying t + -5.5 = 2.872281323 Reorder the terms: -5.5 + t = 2.872281323 Solving -5.5 + t = 2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 2.872281323 + 5.5 t = 2.872281323 + 5.5 Combine like terms: 2.872281323 + 5.5 = 8.372281323 t = 8.372281323 Simplifying t = 8.372281323Subproblem 2
t + -5.5 = -2.872281323 Simplifying t + -5.5 = -2.872281323 Reorder the terms: -5.5 + t = -2.872281323 Solving -5.5 + t = -2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -2.872281323 + 5.5 t = -2.872281323 + 5.5 Combine like terms: -2.872281323 + 5.5 = 2.627718677 t = 2.627718677 Simplifying t = 2.627718677Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.372281323, 2.627718677}
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