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Simplifying t2 + 12t = -5 Reorder the terms: 12t + t2 = -5 Solving 12t + t2 = -5 Solving for variable 't'. Reorder the terms: 5 + 12t + t2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 12t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 12t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12t + t2 = 0 + -5 12t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 12t + t2 = -5 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 = -5 + 36 Reorder the terms: 36 + 12t + t2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + 12t + t2 = 31 Factor a perfect square on the left side: (t + 6)(t + 6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (t + 6) equal to 5.567764363 and -5.567764363.Subproblem 1
t + 6 = 5.567764363 Simplifying t + 6 = 5.567764363 Reorder the terms: 6 + t = 5.567764363 Solving 6 + t = 5.567764363 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 = 5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + t = 5.567764363 + -6 t = 5.567764363 + -6 Combine like terms: 5.567764363 + -6 = -0.432235637 t = -0.432235637 Simplifying t = -0.432235637Subproblem 2
t + 6 = -5.567764363 Simplifying t + 6 = -5.567764363 Reorder the terms: 6 + t = -5.567764363 Solving 6 + t = -5.567764363 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 = -5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + t = -5.567764363 + -6 t = -5.567764363 + -6 Combine like terms: -5.567764363 + -6 = -11.567764363 t = -11.567764363 Simplifying t = -11.567764363Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.432235637, -11.567764363}
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