Answer
(-3,$\sqrt 3$)(-2,2)
Work Step by Step
$ \sqrt {x+6}$ = $\sqrt {-x^{2}-4x }$ Equate the two equations in terms of x since we have the same y in each case
$ {x+6}$ = $ {-x^{2}-4x }$ squaring on both sides
$x^{2} +x +4x+6=0$ moving x terms to one side of the equation
$x^{2} +5x+6=0$ Solving the equation
$(x+2)(x+3)=0$ Solving the equation
$x=-2,x=-3$ we get two values for x
$y=\sqrt {-2+6} =2$ solving for y with x=-2
$y=\sqrt {-3+6} =\sqrt 3$ solving for y with x=-3
And the answer is (-3,$\sqrt 3$)(-2,2)
