radical sign (w + 5) = 2
In all my problems there are a letter variable on the end
example:
radical sign (-u + 30) = u
I then square both sides, drop the radical sign then
(u+6)(u-5)=0
then check to see if they are both true
I guess my question is this is a no solution problem right?
sqrt (36)=-6 checks, so u=-6 is ok
sqrt (25)=5 is ok
Both are solutions. I am wondering why you thought no solution.
To determine if the equation has a solution, we can follow the steps you provided:
1. Start with the equation: radical sign (-u + 30) = u.
2. Square both sides of the equation to eliminate the radical sign:
(-u + 30)^2 = u^2.
Expanding the left side of the equation gives:
u^2 - 60u + 900 = u^2.
3. Simplify the equation by canceling out the u^2 terms:
-60u + 900 = 0.
4. Rearrange the equation to isolate the variable u:
-60u = -900.
Dividing both sides of the equation by -60 gives:
u = 15.
5. Check if the solution is valid by substituting the value of u back into the original equation:
radical sign (-u + 30) = u.
radical sign (-15 + 30) = 15.
radical sign (15) = 15.
The equation holds true, so the solution u = 15 is valid.
Therefore, this problem does have a solution, and it is u = 15.