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Simplifying t2 + -13t + 16 = 0 Reorder the terms: 16 + -13t + t2 = 0 Solving 16 + -13t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -13t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -13t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -13t + t2 = 0 + -16 -13t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -13t + t2 = -16 The t term is -13t. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13t + 42.25 + t2 = -16 + 42.25 Reorder the terms: 42.25 + -13t + t2 = -16 + 42.25 Combine like terms: -16 + 42.25 = 26.25 42.25 + -13t + t2 = 26.25 Factor a perfect square on the left side: (t + -6.5)(t + -6.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (t + -6.5) equal to 5.123475383 and -5.123475383.Subproblem 1
t + -6.5 = 5.123475383 Simplifying t + -6.5 = 5.123475383 Reorder the terms: -6.5 + t = 5.123475383 Solving -6.5 + t = 5.123475383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = 5.123475383 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = 5.123475383 + 6.5 t = 5.123475383 + 6.5 Combine like terms: 5.123475383 + 6.5 = 11.623475383 t = 11.623475383 Simplifying t = 11.623475383Subproblem 2
t + -6.5 = -5.123475383 Simplifying t + -6.5 = -5.123475383 Reorder the terms: -6.5 + t = -5.123475383 Solving -6.5 + t = -5.123475383 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + t = -5.123475383 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + t = -5.123475383 + 6.5 t = -5.123475383 + 6.5 Combine like terms: -5.123475383 + 6.5 = 1.376524617 t = 1.376524617 Simplifying t = 1.376524617Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.623475383, 1.376524617}
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