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Simplifying t2 + -6t + -14 = 0 Reorder the terms: -14 + -6t + t2 = 0 Solving -14 + -6t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -6t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + -6t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6t + t2 = 0 + 14 -6t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 -6t + t2 = 14 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 = 14 + 9 Reorder the terms: 9 + -6t + t2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + -6t + t2 = 23 Factor a perfect square on the left side: (t + -3)(t + -3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (t + -3) equal to 4.795831523 and -4.795831523.Subproblem 1
t + -3 = 4.795831523 Simplifying t + -3 = 4.795831523 Reorder the terms: -3 + t = 4.795831523 Solving -3 + t = 4.795831523 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 = 4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.795831523 + 3 t = 4.795831523 + 3 Combine like terms: 4.795831523 + 3 = 7.795831523 t = 7.795831523 Simplifying t = 7.795831523Subproblem 2
t + -3 = -4.795831523 Simplifying t + -3 = -4.795831523 Reorder the terms: -3 + t = -4.795831523 Solving -3 + t = -4.795831523 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 = -4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.795831523 + 3 t = -4.795831523 + 3 Combine like terms: -4.795831523 + 3 = -1.795831523 t = -1.795831523 Simplifying t = -1.795831523Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.795831523, -1.795831523}
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