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Simplifying t2 + 25t + -24 = 0 Reorder the terms: -24 + 25t + t2 = 0 Solving -24 + 25t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 25t + 24 + t2 = 0 + 24 Reorder the terms: -24 + 24 + 25t + t2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 25t + t2 = 0 + 24 25t + t2 = 0 + 24 Combine like terms: 0 + 24 = 24 25t + t2 = 24 The t term is 25t. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25t + 156.25 + t2 = 24 + 156.25 Reorder the terms: 156.25 + 25t + t2 = 24 + 156.25 Combine like terms: 24 + 156.25 = 180.25 156.25 + 25t + t2 = 180.25 Factor a perfect square on the left side: (t + 12.5)(t + 12.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (t + 12.5) equal to 13.425721582 and -13.425721582.Subproblem 1
t + 12.5 = 13.425721582 Simplifying t + 12.5 = 13.425721582 Reorder the terms: 12.5 + t = 13.425721582 Solving 12.5 + t = 13.425721582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + t = 13.425721582 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + t = 13.425721582 + -12.5 t = 13.425721582 + -12.5 Combine like terms: 13.425721582 + -12.5 = 0.925721582 t = 0.925721582 Simplifying t = 0.925721582Subproblem 2
t + 12.5 = -13.425721582 Simplifying t + 12.5 = -13.425721582 Reorder the terms: 12.5 + t = -13.425721582 Solving 12.5 + t = -13.425721582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + t = -13.425721582 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + t = -13.425721582 + -12.5 t = -13.425721582 + -12.5 Combine like terms: -13.425721582 + -12.5 = -25.925721582 t = -25.925721582 Simplifying t = -25.925721582Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.925721582, -25.925721582}
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