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Simplifying t2 + 16t + 32 = 0 Reorder the terms: 32 + 16t + t2 = 0 Solving 32 + 16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 16t + -32 + t2 = 0 + -32 Reorder the terms: 32 + -32 + 16t + t2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 16t + t2 = 0 + -32 16t + t2 = 0 + -32 Combine like terms: 0 + -32 = -32 16t + t2 = -32 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = -32 + 64 Reorder the terms: 64 + 16t + t2 = -32 + 64 Combine like terms: -32 + 64 = 32 64 + 16t + t2 = 32 Factor a perfect square on the left side: (t + 8)(t + 8) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (t + 8) equal to 5.656854249 and -5.656854249.Subproblem 1
t + 8 = 5.656854249 Simplifying t + 8 = 5.656854249 Reorder the terms: 8 + t = 5.656854249 Solving 8 + t = 5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + t = 5.656854249 + -8 t = 5.656854249 + -8 Combine like terms: 5.656854249 + -8 = -2.343145751 t = -2.343145751 Simplifying t = -2.343145751Subproblem 2
t + 8 = -5.656854249 Simplifying t + 8 = -5.656854249 Reorder the terms: 8 + t = -5.656854249 Solving 8 + t = -5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -5.656854249 + -8 Combine like terms: 8 + -8 = 0 0 + t = -5.656854249 + -8 t = -5.656854249 + -8 Combine like terms: -5.656854249 + -8 = -13.656854249 t = -13.656854249 Simplifying t = -13.656854249Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.343145751, -13.656854249}
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