Answer:
X=7,-4
Explanation:
-3=(37-3x)^(1/2)-x
Add x to each side
X-3=(37-3x)^(1/2)
Change radical to root
X-3=sqrt(37-3x)
Square each side
(X-3)^2=37-3x
Expand the left side: (x-3)*(x-3)=x^2-6x+9
X^2-6x+9=37-3x
Add 3x to each side
X^2-3x+9=37
Subtract 9 from each side
X^2-3x=28
Make it =0: subtract 28 from each side
X^2-3x-28=0
Convert to product form (a)*(b)=0 so that by making either a or b zero you solve the equation. What two numbers add to -3 and multiply to -28? -7 and 4. So we get (x-7)*(x+4).
(X-7)*(x+4)=0
Now we just make x-7=0 or x+4=0.
(7)-7=0 or (-4)+4=0
X=7 or X=-4.