Answer
The solution is $x=1$
Work Step by Step
$x+3x^{1/2}-4=0$
Let $u$ be equal to $x^{1/2}$
If $u=x^{1/2}$, then $u^{2}=x$^
Rewrite the original equation using the new variable $u$:
$u^{2}+3u-4=0$
Solve by factoring:
$(u+4)(u-1)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$u+4=0$
$u=-4$
$u-1=0$
$u=1$
Substitute $u$ back to $x^{1/2}$ and solve for $x$:
$x^{1/2}=-4$
$(x^{1/2})^{2}=(-4)^{2}$
$x=16$
$x^{1/2}=1$
$(x^{1/2})^{2}=1^{2}$
$x=1$
Check the solutions found by plugging them into the original equation:
$x=16$
$16+3(16)^{1/2}-4=0$ False
$x=1$
$1+3(1)^{1/2}-4=0$ True
The solution is $x=1$
