Question

How do you solve `-5sqrt(8x-4) +3 = 18`?

Answer 1

`x in O/`

Explanation:

The idea when dealing with radical equations is to start by isolating the radical term on one side of the equation.

In your case, you can do that by adding `-3` to both sides of the equation and dividing all the terms by `-5`.

`-5sqrt(8x-4) + color(red)(cancel(color(black)(3))) - color(red)(cancel(color(black)(3))) = 18 - 3`

`(color(red)(cancel(color(black)(-5))) sqrt(8x-4))/(color(red)(cancel(color(black)((-5))))) = 15/((-5))`

`sqrt(8x - 4) = -3`

Notice that you have the square root returning a negative value. This cannot happen when dealing with real numbers because you can only take the square root of positive numbers and you will always get a positive number as a result.

This means that the original equation has no real solutions, or `x in O/`.