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Simplifying 2t2 + -12t + 7 = 0 Reorder the terms: 7 + -12t + 2t2 = 0 Solving 7 + -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'. 3.5 + -6t + t2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -6t + -3.5 + t2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -6t + t2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6t + t2 = 0 + -3.5 -6t + t2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6t + t2 = -3.5 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 = -3.5 + 9 Reorder the terms: 9 + -6t + t2 = -3.5 + 9 Combine like terms: -3.5 + 9 = 5.5 9 + -6t + t2 = 5.5 Factor a perfect square on the left side: (t + -3)(t + -3) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (t + -3) equal to 2.34520788 and -2.34520788.Subproblem 1
t + -3 = 2.34520788 Simplifying t + -3 = 2.34520788 Reorder the terms: -3 + t = 2.34520788 Solving -3 + t = 2.34520788 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 = 2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.34520788 + 3 t = 2.34520788 + 3 Combine like terms: 2.34520788 + 3 = 5.34520788 t = 5.34520788 Simplifying t = 5.34520788Subproblem 2
t + -3 = -2.34520788 Simplifying t + -3 = -2.34520788 Reorder the terms: -3 + t = -2.34520788 Solving -3 + t = -2.34520788 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 = -2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.34520788 + 3 t = -2.34520788 + 3 Combine like terms: -2.34520788 + 3 = 0.65479212 t = 0.65479212 Simplifying t = 0.65479212Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.34520788, 0.65479212}
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