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Simplifying t2 + 16t + -43 = 0 Reorder the terms: -43 + 16t + t2 = 0 Solving -43 + 16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 16t + 43 + t2 = 0 + 43 Reorder the terms: -43 + 43 + 16t + t2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 16t + t2 = 0 + 43 16t + t2 = 0 + 43 Combine like terms: 0 + 43 = 43 16t + t2 = 43 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 = 43 + 64 Reorder the terms: 64 + 16t + t2 = 43 + 64 Combine like terms: 43 + 64 = 107 64 + 16t + t2 = 107 Factor a perfect square on the left side: (t + 8)(t + 8) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (t + 8) equal to 10.344080433 and -10.344080433.Subproblem 1
t + 8 = 10.344080433 Simplifying t + 8 = 10.344080433 Reorder the terms: 8 + t = 10.344080433 Solving 8 + t = 10.344080433 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 = 10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + t = 10.344080433 + -8 t = 10.344080433 + -8 Combine like terms: 10.344080433 + -8 = 2.344080433 t = 2.344080433 Simplifying t = 2.344080433Subproblem 2
t + 8 = -10.344080433 Simplifying t + 8 = -10.344080433 Reorder the terms: 8 + t = -10.344080433 Solving 8 + t = -10.344080433 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 = -10.344080433 + -8 Combine like terms: 8 + -8 = 0 0 + t = -10.344080433 + -8 t = -10.344080433 + -8 Combine like terms: -10.344080433 + -8 = -18.344080433 t = -18.344080433 Simplifying t = -18.344080433Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.344080433, -18.344080433}
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