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

Jan 2, 2017

#### Answer:

There is no real solution.

#### Explanation:

By convention ( definition or tradition or practice ),

$\sqrt{a} \ge 0$.

Also, $a \ge 0$ for the radical to be real.

Here,

$\sqrt{5 x + 3} = \left(x + 3\right) \ge 0$, giving $x \succ - 3.$

Also, $a = 5 x + 3 \ge 0$, giving $x \ge - \frac{3}{5}$ that satisfies $x \succ - 3.$

Squaring both sides,

${\left(x + 3\right)}^{2} = 5 x + 3$, 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 $x = - \frac{3}{5}$.

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