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Simplifying 2t2 + 12t + -13 = 0 Reorder the terms: -13 + 12t + 2t2 = 0 Solving -13 + 12t + 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'. -6.5 + 6t + t2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 6t + 6.5 + t2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 6t + t2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 6t + t2 = 0 + 6.5 6t + t2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 6t + t2 = 6.5 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 6.5 + 9 Reorder the terms: 9 + 6t + t2 = 6.5 + 9 Combine like terms: 6.5 + 9 = 15.5 9 + 6t + t2 = 15.5 Factor a perfect square on the left side: (t + 3)(t + 3) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (t + 3) equal to 3.937003937 and -3.937003937.Subproblem 1
t + 3 = 3.937003937 Simplifying t + 3 = 3.937003937 Reorder the terms: 3 + t = 3.937003937 Solving 3 + t = 3.937003937 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 3.937003937 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.937003937 + -3 t = 3.937003937 + -3 Combine like terms: 3.937003937 + -3 = 0.937003937 t = 0.937003937 Simplifying t = 0.937003937Subproblem 2
t + 3 = -3.937003937 Simplifying t + 3 = -3.937003937 Reorder the terms: 3 + t = -3.937003937 Solving 3 + t = -3.937003937 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -3.937003937 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.937003937 + -3 t = -3.937003937 + -3 Combine like terms: -3.937003937 + -3 = -6.937003937 t = -6.937003937 Simplifying t = -6.937003937Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.937003937, -6.937003937}
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