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Simplifying t2 + 24t + -31 = 0 Reorder the terms: -31 + 24t + t2 = 0 Solving -31 + 24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 24t + 31 + t2 = 0 + 31 Reorder the terms: -31 + 31 + 24t + t2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 24t + t2 = 0 + 31 24t + t2 = 0 + 31 Combine like terms: 0 + 31 = 31 24t + t2 = 31 The t term is 24t. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24t + 144 + t2 = 31 + 144 Reorder the terms: 144 + 24t + t2 = 31 + 144 Combine like terms: 31 + 144 = 175 144 + 24t + t2 = 175 Factor a perfect square on the left side: (t + 12)(t + 12) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (t + 12) equal to 13.228756555 and -13.228756555.Subproblem 1
t + 12 = 13.228756555 Simplifying t + 12 = 13.228756555 Reorder the terms: 12 + t = 13.228756555 Solving 12 + t = 13.228756555 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = 13.228756555 + -12 Combine like terms: 12 + -12 = 0 0 + t = 13.228756555 + -12 t = 13.228756555 + -12 Combine like terms: 13.228756555 + -12 = 1.228756555 t = 1.228756555 Simplifying t = 1.228756555Subproblem 2
t + 12 = -13.228756555 Simplifying t + 12 = -13.228756555 Reorder the terms: 12 + t = -13.228756555 Solving 12 + t = -13.228756555 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = -13.228756555 + -12 Combine like terms: 12 + -12 = 0 0 + t = -13.228756555 + -12 t = -13.228756555 + -12 Combine like terms: -13.228756555 + -12 = -25.228756555 t = -25.228756555 Simplifying t = -25.228756555Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.228756555, -25.228756555}
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