Question

Solve: √ 2w+8=−w. If there are multiple solutions, list them separated by a comma, e.g., 1,2. If there is no real solution, enter ∅.

Answer 1

Given the equation

`\sqrt[]{2w+8}=-w`

To solve the question, we will follow the steps below:

Step 1: square both sides

`2w+8=(-w)^2`

Step 2: Simplify the expression

`2w+8=w^2`
`w^2-2w-8=0`

simplifying further

`(w+2)(w-4)=0`

Finding the zeros gives

`\begin{gathered} w=-2\text{ } \\ or \\ w=4 \end{gathered}`

Hence

The solutions are: -2,4