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Simplifying (5t + -8) + (t2 + 6t + 12) = 0 Reorder the terms: (-8 + 5t) + (t2 + 6t + 12) = 0 Remove parenthesis around (-8 + 5t) -8 + 5t + (t2 + 6t + 12) = 0 Reorder the terms: -8 + 5t + (12 + 6t + t2) = 0 Remove parenthesis around (12 + 6t + t2) -8 + 5t + 12 + 6t + t2 = 0 Reorder the terms: -8 + 12 + 5t + 6t + t2 = 0 Combine like terms: -8 + 12 = 4 4 + 5t + 6t + t2 = 0 Combine like terms: 5t + 6t = 11t 4 + 11t + t2 = 0 Solving 4 + 11t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 11t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 11t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11t + t2 = 0 + -4 11t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 11t + t2 = -4 The t term is 11t. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11t + 30.25 + t2 = -4 + 30.25 Reorder the terms: 30.25 + 11t + t2 = -4 + 30.25 Combine like terms: -4 + 30.25 = 26.25 30.25 + 11t + t2 = 26.25 Factor a perfect square on the left side: (t + 5.5)(t + 5.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (t + 5.5) equal to 5.123475383 and -5.123475383.Subproblem 1
t + 5.5 = 5.123475383 Simplifying t + 5.5 = 5.123475383 Reorder the terms: 5.5 + t = 5.123475383 Solving 5.5 + t = 5.123475383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = 5.123475383 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = 5.123475383 + -5.5 t = 5.123475383 + -5.5 Combine like terms: 5.123475383 + -5.5 = -0.376524617 t = -0.376524617 Simplifying t = -0.376524617Subproblem 2
t + 5.5 = -5.123475383 Simplifying t + 5.5 = -5.123475383 Reorder the terms: 5.5 + t = -5.123475383 Solving 5.5 + t = -5.123475383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + t = -5.123475383 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + t = -5.123475383 + -5.5 t = -5.123475383 + -5.5 Combine like terms: -5.123475383 + -5.5 = -10.623475383 t = -10.623475383 Simplifying t = -10.623475383Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.376524617, -10.623475383}
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