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Simplifying t2 + -12t + 8 = 0 Reorder the terms: 8 + -12t + t2 = 0 Solving 8 + -12t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -12t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + -12t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -12t + t2 = 0 + -8 -12t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -12t + t2 = -8 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -8 + 36 Reorder the terms: 36 + -12t + t2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + -12t + t2 = 28 Factor a perfect square on the left side: (t + -6)(t + -6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (t + -6) equal to 5.291502622 and -5.291502622.Subproblem 1
t + -6 = 5.291502622 Simplifying t + -6 = 5.291502622 Reorder the terms: -6 + t = 5.291502622 Solving -6 + t = 5.291502622 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + t = 5.291502622 + 6 t = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 t = 11.291502622 Simplifying t = 11.291502622Subproblem 2
t + -6 = -5.291502622 Simplifying t + -6 = -5.291502622 Reorder the terms: -6 + t = -5.291502622 Solving -6 + t = -5.291502622 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + t = -5.291502622 + 6 t = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 t = 0.708497378 Simplifying t = 0.708497378Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.291502622, 0.708497378}
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