Question

What is the solution set of the quadratic equation 8x2 +2x +1 =0?

Answer 1

`\displaystyle\\ 8x^2 +2x +1 =0\\\\ x_(12)=(-b\pm √(b^2-4ac))/(2a)=(-2\pm √(2^2-4\cdot 8 \cdot 1))/(2\cdot 8)=\\\\ =(-2\pm √(4-32))/(16)=(-2\pm √(-28))/(16)=(-2\pm √(4\cdot 7\cdot(-1)))/(16)=\\\\ =(-2\pm 2i√(7))/(16)=(-1\pm i√(7))/(8)= -(1)/(8)\pm (√(7))/(8)i\\\\ x_1 = \boxed{-(1)/(8)+ (√(7))/(8)i}\\\\ x_2 = \boxed{-(1)/(8)- (√(7))/(8)i}\\\\ x_1,~x_2~\in \mathbb{C}`