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Simplifying 2t2 + -12t + 14 = 0 Reorder the terms: 14 + -12t + 2t2 = 0 Solving 14 + -12t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -6t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -6t + t2)' equal to zero and attempt to solve: Simplifying 7 + -6t + t2 = 0 Solving 7 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -6t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6t + t2 = 0 + -7 -6t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6t + t2 = -7 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 = -7 + 9 Reorder the terms: 9 + -6t + t2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6t + t2 = 2 Factor a perfect square on the left side: (t + -3)(t + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
t + -3 = 1.414213562 Simplifying t + -3 = 1.414213562 Reorder the terms: -3 + t = 1.414213562 Solving -3 + t = 1.414213562 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 = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.414213562 + 3 t = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 t = 4.414213562 Simplifying t = 4.414213562Subproblem 2
t + -3 = -1.414213562 Simplifying t + -3 = -1.414213562 Reorder the terms: -3 + t = -1.414213562 Solving -3 + t = -1.414213562 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 = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.414213562 + 3 t = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 t = 1.585786438 Simplifying t = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.414213562, 1.585786438}Solution
t = {4.414213562, 1.585786438}
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