Question

In the following exercises, solve by using the Quadratic Formula.

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

Short answer

The solution of the given equation is $y=-\frac{1}{4}$.

Step-by-step solution

Step 1. Given information.

The given equation is:

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

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In the given equation, $a=16,b=8,c=1$. Substitute these values in Quadratic Formula.

$y=\frac{-8\pm \sqrt{(8{)}^2-4(16\left)\right(1)}}{2\left(16\right)}$

Step 3. Simplify the value.

On simplification, we get

$$\begin{gathered} y=\frac{-8\pm \sqrt{64-64}}{32} \\ y=\frac{-8\pm 0}{32} \\ y=\frac{-8}{32} \\ y=-\frac{1}{4} \end{gathered}$$

Step 4. Conclusion.

The solution of the given equation is $y=-\frac{1}{4}$.