Question

In the following exercises, solve by using the Quadratic Formula.
$y^2+4y-4=0$

Short answer

The solutions of the given equation are $y=-2\pm 2\sqrt{2}$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$y^2+4y-4=0$

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, $a=1,b=4,c=-4$. Substitute these values in Quadratic Formula.

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

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl}y& =& \frac{-4\pm \sqrt{16+16}}{2}\\ y& =& \frac{-4\pm \sqrt{32}}{2}\\ y& =& \frac{-4}{2}\pm \frac{4\sqrt{2}}{2}\\ y& =& -2\pm 2\sqrt{2}\end{array}$

Step 4. Conclusion.

The solutions of the given equation are $y=-2\pm 2\sqrt{2}$.