SOLUTION: How do you find out if an equation has real numbers? For example, x^2-9=0, x^2+7=1, 3x-7=14, which one has no real solutions?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How do you find out if an equation has real numbers? For example, x^2-9=0, x^2+7=1, 3x-7=14, which one has no real solutions?      Log On


   

Question 755056: How do you find out if an equation has real numbers? For example, x^2-9=0, x^2+7=1, 3x-7=14, which one has no real solutions?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If there is a +sqrt%28-1%29+ in the solutions, then
the solutions are not all real.
(a)
+x%5E2+-+9+=+0+
Add 9 to both sides
+x%5E2+=+9+
+x+=+3+
and
+x+=+-3+
Both are real solutions
-------------------
(b)
+x%5E2+%2B+7+=+1+
Subtract +7+ from both sides
+x%5E2+=+-6+
+x+=+sqrt%28-1%29%2Asqrt%286%29+
+x+=+sqrt%286%29%2Ai+
and also,
+x+=+-%28+sqrt%28-1%29%2Asqrt%286%29+%29+
+x+=+-sqrt%286%29%2Ai+
There are no real solutions
-----------------------
(c)
+3x+-+7+=+14+
+3x+=+21+
+x+=+7+
There is 1 real solution