Question

What is the solution set for the equation `sqrt(5x+29)=x+3`?

Answer 1

There is no real solution.

Explanation:

By convention ( definition or tradition or practice ),

`sqrt(a) >=0`.

Also, `a >=0` for the radical to be real.

Here,

`sqrt(5x+3)=(x+3) >=0`, giving `x >--3.`

Also, `a = 5x + 3 >=0`, giving `x >=-3/5` that satisfies `x >--3.`

Squaring both sides,

`(x+3)^2=5x+3`, giving

`x^2+x+6=0`.

The zeros are complex.

So, there is no real solution.

In the Socratic graph, see that the graph does not cut the x-axis,

Look at the dead end at `x = -3/5`.

graph{sqrt(5x+3)-x-3 [-15.06, 15.07, -7.53, 7.53]}