Question

Solve each equation by using the root property. x^2+4x+4=3

Answer 1

The left side of the equation is a notable product. The sum of two squares. We an factor it by adding the root of the first term by the root of the third and powering it by 2. We have:

`\begin{gathered} x^2+4x+4=3 \\ (x+2)^2=3 \end{gathered}`

We can now apply the root property. This is done by taking the square root on both sides.

`\begin{gathered} \sqrt[]{(x+2)^2}=\sqrt[]{3} \\ x+2=\pm3 \\ x=-2\pm3 \end{gathered}`
`\begin{gathered} x_1=-2-3=-5 \\ x_2=-2+3=1 \end{gathered}`

The two solutions are "1" and "-5".