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Simplifying 2t2 + 11t + -35 = 0 Reorder the terms: -35 + 11t + 2t2 = 0 Solving -35 + 11t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 5.5t + t2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 5.5t + 17.5 + t2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 5.5t + t2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 5.5t + t2 = 0 + 17.5 5.5t + t2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 5.5t + t2 = 17.5 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 = 17.5 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 17.5 + 7.5625 Combine like terms: 17.5 + 7.5625 = 25.0625 7.5625 + 5.5t + t2 = 25.0625 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (t + 2.75) equal to 5.006246099 and -5.006246099.Subproblem 1
t + 2.75 = 5.006246099 Simplifying t + 2.75 = 5.006246099 Reorder the terms: 2.75 + t = 5.006246099 Solving 2.75 + t = 5.006246099 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 = 5.006246099 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 5.006246099 + -2.75 t = 5.006246099 + -2.75 Combine like terms: 5.006246099 + -2.75 = 2.256246099 t = 2.256246099 Simplifying t = 2.256246099Subproblem 2
t + 2.75 = -5.006246099 Simplifying t + 2.75 = -5.006246099 Reorder the terms: 2.75 + t = -5.006246099 Solving 2.75 + t = -5.006246099 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 = -5.006246099 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -5.006246099 + -2.75 t = -5.006246099 + -2.75 Combine like terms: -5.006246099 + -2.75 = -7.756246099 t = -7.756246099 Simplifying t = -7.756246099Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.256246099, -7.756246099}
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