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Simplifying 2t2 + 13t = 6 Reorder the terms: 13t + 2t2 = 6 Solving 13t + 2t2 = 6 Solving for variable 't'. Reorder the terms: -6 + 13t + 2t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 13t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 6.5t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6.5t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 6.5t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6.5t + t2 = 0 + 3 6.5t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 6.5t + t2 = 3 The t term is 6.5t. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5t + 10.5625 + t2 = 3 + 10.5625 Reorder the terms: 10.5625 + 6.5t + t2 = 3 + 10.5625 Combine like terms: 3 + 10.5625 = 13.5625 10.5625 + 6.5t + t2 = 13.5625 Factor a perfect square on the left side: (t + 3.25)(t + 3.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (t + 3.25) equal to 3.682729966 and -3.682729966.Subproblem 1
t + 3.25 = 3.682729966 Simplifying t + 3.25 = 3.682729966 Reorder the terms: 3.25 + t = 3.682729966 Solving 3.25 + t = 3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + t = 3.682729966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + t = 3.682729966 + -3.25 t = 3.682729966 + -3.25 Combine like terms: 3.682729966 + -3.25 = 0.432729966 t = 0.432729966 Simplifying t = 0.432729966Subproblem 2
t + 3.25 = -3.682729966 Simplifying t + 3.25 = -3.682729966 Reorder the terms: 3.25 + t = -3.682729966 Solving 3.25 + t = -3.682729966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + t = -3.682729966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + t = -3.682729966 + -3.25 t = -3.682729966 + -3.25 Combine like terms: -3.682729966 + -3.25 = -6.932729966 t = -6.932729966 Simplifying t = -6.932729966Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.432729966, -6.932729966}
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