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Simplifying t2 + 13t + 49 = 25 Reorder the terms: 49 + 13t + t2 = 25 Solving 49 + 13t + t2 = 25 Solving for variable 't'. Reorder the terms: 49 + -25 + 13t + t2 = 25 + -25 Combine like terms: 49 + -25 = 24 24 + 13t + t2 = 25 + -25 Combine like terms: 25 + -25 = 0 24 + 13t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 13t + -24 + t2 = 0 + -24 Reorder the terms: 24 + -24 + 13t + t2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 13t + t2 = 0 + -24 13t + t2 = 0 + -24 Combine like terms: 0 + -24 = -24 13t + t2 = -24 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 = -24 + 42.25 Reorder the terms: 42.25 + 13t + t2 = -24 + 42.25 Combine like terms: -24 + 42.25 = 18.25 42.25 + 13t + t2 = 18.25 Factor a perfect square on the left side: (t + 6.5)(t + 6.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (t + 6.5) equal to 4.272001873 and -4.272001873.Subproblem 1
t + 6.5 = 4.272001873 Simplifying t + 6.5 = 4.272001873 Reorder the terms: 6.5 + t = 4.272001873 Solving 6.5 + t = 4.272001873 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 = 4.272001873 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = 4.272001873 + -6.5 t = 4.272001873 + -6.5 Combine like terms: 4.272001873 + -6.5 = -2.227998127 t = -2.227998127 Simplifying t = -2.227998127Subproblem 2
t + 6.5 = -4.272001873 Simplifying t + 6.5 = -4.272001873 Reorder the terms: 6.5 + t = -4.272001873 Solving 6.5 + t = -4.272001873 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 = -4.272001873 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = -4.272001873 + -6.5 t = -4.272001873 + -6.5 Combine like terms: -4.272001873 + -6.5 = -10.772001873 t = -10.772001873 Simplifying t = -10.772001873Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.227998127, -10.772001873}
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