Question

Solve the equation 4x2 + 8x + 1 = 0 by completing the square. Verify your answer using the quadratic formula.

Answer 1

Given:

$4x^2+8x+1=0$

$\begin{gathered} x^2+2x+\frac{1}{4}=0 \\ x^2+2x+1-1+\frac{1}{4}=0 \\ (x+1)^2=1-\frac{1}{4} \\ (x+1)^2=\frac{3}{4} \end{gathered}$

Taking square root on both sides

$\begin{gathered} x+1=\pm\frac{\sqrt[]{3}}{2} \\ x=-1\pm\frac{\sqrt[]{3}}{2} \\ x=\frac{-2\pm\sqrt[]{3}}{2} \end{gathered}$

3rd option is the final answer