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Simplifying 3 + 2 + 8t = t2 + -3t + -12 Combine like terms: 3 + 2 = 5 5 + 8t = t2 + -3t + -12 Reorder the terms: 5 + 8t = -12 + -3t + t2 Solving 5 + 8t = -12 + -3t + t2 Solving for variable 't'. Reorder the terms: 5 + 12 + 8t + 3t + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2 Combine like terms: 5 + 12 = 17 17 + 8t + 3t + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2 Combine like terms: 8t + 3t = 11t 17 + 11t + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2 Reorder the terms: 17 + 11t + -1t2 = -12 + 12 + -3t + 3t + t2 + -1t2 Combine like terms: -12 + 12 = 0 17 + 11t + -1t2 = 0 + -3t + 3t + t2 + -1t2 17 + 11t + -1t2 = -3t + 3t + t2 + -1t2 Combine like terms: -3t + 3t = 0 17 + 11t + -1t2 = 0 + t2 + -1t2 17 + 11t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 17 + 11t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -11t + t2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -11t + 17 + t2 = 0 + 17 Reorder the terms: -17 + 17 + -11t + t2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -11t + t2 = 0 + 17 -11t + t2 = 0 + 17 Combine like terms: 0 + 17 = 17 -11t + t2 = 17 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 = 17 + 30.25 Reorder the terms: 30.25 + -11t + t2 = 17 + 30.25 Combine like terms: 17 + 30.25 = 47.25 30.25 + -11t + t2 = 47.25 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (t + -5.5) equal to 6.873863542 and -6.873863542.Subproblem 1
t + -5.5 = 6.873863542 Simplifying t + -5.5 = 6.873863542 Reorder the terms: -5.5 + t = 6.873863542 Solving -5.5 + t = 6.873863542 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 = 6.873863542 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 6.873863542 + 5.5 t = 6.873863542 + 5.5 Combine like terms: 6.873863542 + 5.5 = 12.373863542 t = 12.373863542 Simplifying t = 12.373863542Subproblem 2
t + -5.5 = -6.873863542 Simplifying t + -5.5 = -6.873863542 Reorder the terms: -5.5 + t = -6.873863542 Solving -5.5 + t = -6.873863542 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 = -6.873863542 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -6.873863542 + 5.5 t = -6.873863542 + 5.5 Combine like terms: -6.873863542 + 5.5 = -1.373863542 t = -1.373863542 Simplifying t = -1.373863542Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.373863542, -1.373863542}
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