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Simplifying t2 + -4 = 6t + 8 Reorder the terms: -4 + t2 = 6t + 8 Reorder the terms: -4 + t2 = 8 + 6t Solving -4 + t2 = 8 + 6t Solving for variable 't'. Reorder the terms: -4 + -8 + -6t + t2 = 8 + 6t + -8 + -6t Combine like terms: -4 + -8 = -12 -12 + -6t + t2 = 8 + 6t + -8 + -6t Reorder the terms: -12 + -6t + t2 = 8 + -8 + 6t + -6t Combine like terms: 8 + -8 = 0 -12 + -6t + t2 = 0 + 6t + -6t -12 + -6t + t2 = 6t + -6t Combine like terms: 6t + -6t = 0 -12 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -6t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -6t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6t + t2 = 0 + 12 -6t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6t + t2 = 12 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 = 12 + 9 Reorder the terms: 9 + -6t + t2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + -6t + t2 = 21 Factor a perfect square on the left side: (t + -3)(t + -3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + -3) equal to 4.582575695 and -4.582575695.Subproblem 1
t + -3 = 4.582575695 Simplifying t + -3 = 4.582575695 Reorder the terms: -3 + t = 4.582575695 Solving -3 + t = 4.582575695 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 = 4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.582575695 + 3 t = 4.582575695 + 3 Combine like terms: 4.582575695 + 3 = 7.582575695 t = 7.582575695 Simplifying t = 7.582575695Subproblem 2
t + -3 = -4.582575695 Simplifying t + -3 = -4.582575695 Reorder the terms: -3 + t = -4.582575695 Solving -3 + t = -4.582575695 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 = -4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.582575695 + 3 t = -4.582575695 + 3 Combine like terms: -4.582575695 + 3 = -1.582575695 t = -1.582575695 Simplifying t = -1.582575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.582575695, -1.582575695}
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