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+(1)/(4)=0 \\ x^2+2x+1-1+(1)/(4)=0 \\ (x+1)^2=1-(1)/(4) \\ (x+1)^2=(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