Question

Solve the equation using quadratic formula.

$16y^2+8y+1=0$

Short answer

The roots are$y=\frac{-1}{4}$.

Step-by-step solution

 Given Information.  

The given equation is$16y^2+8y+1=0$.

Write the quadratic equation in standard form and identify a,b,c.

$16y^2+8y+1=0$

The equation is in standard form.

So,

$a=16,b=8,c=1$

Substitute the values in quadratic formula.      

$$\begin{gathered} y=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ y=\frac{-8\pm \sqrt{(8{)}^2-4(16\left)\right(1)}}{2\left(16\right)} \\ y=\frac{-8\pm \sqrt{64-64}}{32} \end{gathered}$$

Use square root property.  

$$\begin{gathered} y=\frac{-8\pm \sqrt{0}}{32} \\ y=\frac{-8}{32} \\ y=\frac{-1}{4} \end{gathered}$$

Thus, the root is$y=\frac{-1}{4}$.