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Simplifying t2 + 5t + -12 = 0 Reorder the terms: -12 + 5t + t2 = 0 Solving -12 + 5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 5t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + 5t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5t + t2 = 0 + 12 5t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 5t + t2 = 12 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 12 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + 5t + t2 = 18.25 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (t + 2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
t + 2.5 = 4.272001873 Simplifying t + 2.5 = 4.272001873 Reorder the terms: 2.5 + t = 4.272001873 Solving 2.5 + t = 4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 4.272001873 + -2.5 t = 4.272001873 + -2.5 Combine like terms: 4.272001873 + -2.5 = 1.772001873 t = 1.772001873 Simplifying t = 1.772001873Subproblem 2
t + 2.5 = -4.272001873 Simplifying t + 2.5 = -4.272001873 Reorder the terms: 2.5 + t = -4.272001873 Solving 2.5 + t = -4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -4.272001873 + -2.5 t = -4.272001873 + -2.5 Combine like terms: -4.272001873 + -2.5 = -6.772001873 t = -6.772001873 Simplifying t = -6.772001873Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.772001873, -6.772001873}
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