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Simplifying t * t + 24t + 60 = 0 Multiply t * t t2 + 24t + 60 = 0 Reorder the terms: 60 + 24t + t2 = 0 Solving 60 + 24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 24t + -60 + t2 = 0 + -60 Reorder the terms: 60 + -60 + 24t + t2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 24t + t2 = 0 + -60 24t + t2 = 0 + -60 Combine like terms: 0 + -60 = -60 24t + t2 = -60 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 = -60 + 144 Reorder the terms: 144 + 24t + t2 = -60 + 144 Combine like terms: -60 + 144 = 84 144 + 24t + t2 = 84 Factor a perfect square on the left side: (t + 12)(t + 12) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (t + 12) equal to 9.16515139 and -9.16515139.Subproblem 1
t + 12 = 9.16515139 Simplifying t + 12 = 9.16515139 Reorder the terms: 12 + t = 9.16515139 Solving 12 + t = 9.16515139 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 = 9.16515139 + -12 Combine like terms: 12 + -12 = 0 0 + t = 9.16515139 + -12 t = 9.16515139 + -12 Combine like terms: 9.16515139 + -12 = -2.83484861 t = -2.83484861 Simplifying t = -2.83484861Subproblem 2
t + 12 = -9.16515139 Simplifying t + 12 = -9.16515139 Reorder the terms: 12 + t = -9.16515139 Solving 12 + t = -9.16515139 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 = -9.16515139 + -12 Combine like terms: 12 + -12 = 0 0 + t = -9.16515139 + -12 t = -9.16515139 + -12 Combine like terms: -9.16515139 + -12 = -21.16515139 t = -21.16515139 Simplifying t = -21.16515139Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.83484861, -21.16515139}
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