Question 162836: Please help!!!
I am trying to solve this problem and I'm stuck.
the square root of (x+6) + 1 = the square root of (2x-11)
Thanks in Advance!
Answer by joecbaseball(37)   (Show Source):
You can put this solution on YOUR website! Don't make this harder than it is. Remember, to eliminate square roots, you have to square terms if they don't drop out in the course of doing the problem. In this case, you have to square both sides two times. This is how it is done:
Your problem is:
Sqrt (x + 6) + 1 = sqrt (2x – 11)
Square both sides and get:
(x + 6) + 2(sqrt (x + 6)) + 1 = (2x – 11)
Now simplify:
x + 7 + 2(sqrt (x + 6)) = 2x – 11
Subtract an x and 7 from both sides to get the sqrt by itself. This gives you:
2(sqrt(x + 6)) = x – 18
Now square both sides again. This gives you:
4(x + 6) = (x – 18)^2
Now, distribute on the left hand side and expand on the right hand side. This gives you:
4x + 24 = x^2 - 36x + 324
Now get all terms on one side and set equation equal to zero. This gives you:
0 = x^2 – 40x + 300 OR x^2 – 40x + 300 = 0. These are the same, but most students prefer the second one.
Now, either factor or use the quadratic formula to get x = 10 and x = 30
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