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Simplifying t2 + 16t + -4 = 0 Reorder the terms: -4 + 16t + t2 = 0 Solving -4 + 16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 16t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + 16t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 16t + t2 = 0 + 4 16t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 16t + t2 = 4 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 = 4 + 64 Reorder the terms: 64 + 16t + t2 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + 16t + t2 = 68 Factor a perfect square on the left side: (t + 8)(t + 8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (t + 8) equal to 8.246211251 and -8.246211251.Subproblem 1
t + 8 = 8.246211251 Simplifying t + 8 = 8.246211251 Reorder the terms: 8 + t = 8.246211251 Solving 8 + t = 8.246211251 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 = 8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + t = 8.246211251 + -8 t = 8.246211251 + -8 Combine like terms: 8.246211251 + -8 = 0.246211251 t = 0.246211251 Simplifying t = 0.246211251Subproblem 2
t + 8 = -8.246211251 Simplifying t + 8 = -8.246211251 Reorder the terms: 8 + t = -8.246211251 Solving 8 + t = -8.246211251 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 = -8.246211251 + -8 Combine like terms: 8 + -8 = 0 0 + t = -8.246211251 + -8 t = -8.246211251 + -8 Combine like terms: -8.246211251 + -8 = -16.246211251 t = -16.246211251 Simplifying t = -16.246211251Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.246211251, -16.246211251}
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