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Simplifying 2t2 + 11t = 8 Reorder the terms: 11t + 2t2 = 8 Solving 11t + 2t2 = 8 Solving for variable 't'. Reorder the terms: -8 + 11t + 2t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 11t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 5.5t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 5.5t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 5.5t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5.5t + t2 = 0 + 4 5.5t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 5.5t + t2 = 4 The t term is 5.5t. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5t + 7.5625 + t2 = 4 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 4 + 7.5625 Combine like terms: 4 + 7.5625 = 11.5625 7.5625 + 5.5t + t2 = 11.5625 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (t + 2.75) equal to 3.400367627 and -3.400367627.Subproblem 1
t + 2.75 = 3.400367627 Simplifying t + 2.75 = 3.400367627 Reorder the terms: 2.75 + t = 3.400367627 Solving 2.75 + t = 3.400367627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = 3.400367627 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 3.400367627 + -2.75 t = 3.400367627 + -2.75 Combine like terms: 3.400367627 + -2.75 = 0.650367627 t = 0.650367627 Simplifying t = 0.650367627Subproblem 2
t + 2.75 = -3.400367627 Simplifying t + 2.75 = -3.400367627 Reorder the terms: 2.75 + t = -3.400367627 Solving 2.75 + t = -3.400367627 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = -3.400367627 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -3.400367627 + -2.75 t = -3.400367627 + -2.75 Combine like terms: -3.400367627 + -2.75 = -6.150367627 t = -6.150367627 Simplifying t = -6.150367627Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.650367627, -6.150367627}
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