Answer
x = 1
Work Step by Step
Add $1$ to both sides.
$(x+3)^{1/2} = x + 1$
Square both sides of the equation to remove the square root.
$\left((x + 3)^{1/2}\right)^2 = (x+1)^2\\
x+3=x^{2} + 2x + 1$
Subtract the left side of the equation so that the right side is set equal to 0.
$0 = x^{2} + 2x + 1 - (x + 3)\\
0 = x^{2} + 2x + 1 - x-3$
Combine like terms.
$0 = x^{2} + x - 2$
Factor out the equation.
$0 = (x + 2)(x - 1)$
Set each factor equal to zero and solve for x.
$x + 2 = 0 \rightarrow x = -2$
$x - 1 = 0 \rightarrow x = 1$
Check the answers for extraneous solutions. Does the answer make the original statement true?
$(-2+3)^{1/2} - 1 = -2$
$1 - 1 = -2$
$ 0 =-2$
Since the statement is not true, $x=-2$ is an extraneous solution.
Check the second answer for an extraneous solution.
$(1+3)^{1/2} - 1 = 1$
$2 - 1 = 1$
$1 = 1$
Since the original statement is true, we can conclude that $x = 1$ is a solution.
