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

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Answer 1 · 2017-01-02T14:35:22

There is no real solution.

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]}