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Simplifying t2 + 12t = 32 Reorder the terms: 12t + t2 = 32 Solving 12t + t2 = 32 Solving for variable 't'. Reorder the terms: -32 + 12t + t2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 12t + 32 + t2 = 0 + 32 Reorder the terms: -32 + 32 + 12t + t2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 12t + t2 = 0 + 32 12t + t2 = 0 + 32 Combine like terms: 0 + 32 = 32 12t + t2 = 32 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 = 32 + 36 Reorder the terms: 36 + 12t + t2 = 32 + 36 Combine like terms: 32 + 36 = 68 36 + 12t + t2 = 68 Factor a perfect square on the left side: (t + 6)(t + 6) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (t + 6) equal to 8.246211251 and -8.246211251.Subproblem 1
t + 6 = 8.246211251 Simplifying t + 6 = 8.246211251 Reorder the terms: 6 + t = 8.246211251 Solving 6 + t = 8.246211251 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 = 8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + t = 8.246211251 + -6 t = 8.246211251 + -6 Combine like terms: 8.246211251 + -6 = 2.246211251 t = 2.246211251 Simplifying t = 2.246211251Subproblem 2
t + 6 = -8.246211251 Simplifying t + 6 = -8.246211251 Reorder the terms: 6 + t = -8.246211251 Solving 6 + t = -8.246211251 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 = -8.246211251 + -6 Combine like terms: 6 + -6 = 0 0 + t = -8.246211251 + -6 t = -8.246211251 + -6 Combine like terms: -8.246211251 + -6 = -14.246211251 t = -14.246211251 Simplifying t = -14.246211251Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.246211251, -14.246211251}
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