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Simplifying 0 = 16t2 + -29t + -124 Reorder the terms: 0 = -124 + -29t + 16t2 Solving 0 = -124 + -29t + 16t2 Solving for variable 't'. Combine like terms: 0 + 124 = 124 124 + 29t + -16t2 = -124 + -29t + 16t2 + 124 + 29t + -16t2 Reorder the terms: 124 + 29t + -16t2 = -124 + 124 + -29t + 29t + 16t2 + -16t2 Combine like terms: -124 + 124 = 0 124 + 29t + -16t2 = 0 + -29t + 29t + 16t2 + -16t2 124 + 29t + -16t2 = -29t + 29t + 16t2 + -16t2 Combine like terms: -29t + 29t = 0 124 + 29t + -16t2 = 0 + 16t2 + -16t2 124 + 29t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 124 + 29t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7.75 + -1.8125t + t2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + -1.8125t + 7.75 + t2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + -1.8125t + t2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + -1.8125t + t2 = 0 + 7.75 -1.8125t + t2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 -1.8125t + t2 = 7.75 The t term is -1.8125t. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125t + 0.8212890625 + t2 = 7.75 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125t + t2 = 7.75 + 0.8212890625 Combine like terms: 7.75 + 0.8212890625 = 8.5712890625 0.8212890625 + -1.8125t + t2 = 8.5712890625 Factor a perfect square on the left side: (t + -0.90625)(t + -0.90625) = 8.5712890625 Calculate the square root of the right side: 2.927676393 Break this problem into two subproblems by setting (t + -0.90625) equal to 2.927676393 and -2.927676393.Subproblem 1
t + -0.90625 = 2.927676393 Simplifying t + -0.90625 = 2.927676393 Reorder the terms: -0.90625 + t = 2.927676393 Solving -0.90625 + t = 2.927676393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = 2.927676393 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = 2.927676393 + 0.90625 t = 2.927676393 + 0.90625 Combine like terms: 2.927676393 + 0.90625 = 3.833926393 t = 3.833926393 Simplifying t = 3.833926393Subproblem 2
t + -0.90625 = -2.927676393 Simplifying t + -0.90625 = -2.927676393 Reorder the terms: -0.90625 + t = -2.927676393 Solving -0.90625 + t = -2.927676393 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + t = -2.927676393 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + t = -2.927676393 + 0.90625 t = -2.927676393 + 0.90625 Combine like terms: -2.927676393 + 0.90625 = -2.021426393 t = -2.021426393 Simplifying t = -2.021426393Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.833926393, -2.021426393}
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