# How do you solve sqrt(4x+1)+3=0?

Mar 16, 2018

You can't.

#### Explanation:

$\sqrt{4 x + 1} + 3 = 0$

Subtract $- 3$ from both sides,

$\sqrt{4 x + 1} = - 3$

Since the square root of any number cannot be negative, there are no values of $x$ that satisfies the equation.

Mar 25, 2018

Actually, there is no solution.

#### Explanation:

I know everyone else said that the solution is $x = 2$, but if you plug it in, it doesn't hold up:

$\textcolor{w h i t e}{\implies} \sqrt{4 x + 1} + 3 = 0$

$\implies \sqrt{4 \left(2\right) + 1} + 3 = 0$

$\textcolor{w h i t e}{\implies} \sqrt{8 + 1} + 3 = 0$

$\textcolor{w h i t e}{\implies} \sqrt{9} + 3 = 0$

$\textcolor{w h i t e}{\implies} 3 + 3 = 0$

$\textcolor{w h i t e}{\implies} 6 \ne 0$

You can also look at the graph of $\sqrt{4 x + 1} + 3$ and see that there are no zeroes:

graph{sqrt(4x+1)+3 [-10.24, 15.07, -3.37, 9.29]}

Here's the flaw in trying to solve it:

$\sqrt{4 x + 1} + 3 = 0$

$\sqrt{4 x + 1} = - 3$
$\text{ } \textcolor{red}{\uparrow}$
Here's the mistake. A square root cannot equal a negative number, so the process needs to stop here. Unfortunately, you can't square both sides.

Hope this helped!