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Simplifying t2 + 9t + 6 = 0 Reorder the terms: 6 + 9t + t2 = 0 Solving 6 + 9t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + 9t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9t + t2 = 0 + -6 9t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 9t + t2 = -6 The t term is 9t. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9t + 20.25 + t2 = -6 + 20.25 Reorder the terms: 20.25 + 9t + t2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + 9t + t2 = 14.25 Factor a perfect square on the left side: (t + 4.5)(t + 4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (t + 4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
t + 4.5 = 3.774917218 Simplifying t + 4.5 = 3.774917218 Reorder the terms: 4.5 + t = 3.774917218 Solving 4.5 + t = 3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = 3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = 3.774917218 + -4.5 t = 3.774917218 + -4.5 Combine like terms: 3.774917218 + -4.5 = -0.725082782 t = -0.725082782 Simplifying t = -0.725082782Subproblem 2
t + 4.5 = -3.774917218 Simplifying t + 4.5 = -3.774917218 Reorder the terms: 4.5 + t = -3.774917218 Solving 4.5 + t = -3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = -3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = -3.774917218 + -4.5 t = -3.774917218 + -4.5 Combine like terms: -3.774917218 + -4.5 = -8.274917218 t = -8.274917218 Simplifying t = -8.274917218Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.725082782, -8.274917218}
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