Question 111763This question is from textbook College Algebra
: Hey, can someone help me please?
Radical equations and graphs:
Solve for x
√(x+7) +5=x
This is what I have so far: √(x+7 ) =x-5
(√(x+7))^2= (x-5)^2
x+7= x^2+25x+7
This question is from textbook College Algebra
Found 2 solutions by Osterm38, freedom1:
Answer by Osterm38(2)   (Show Source):
You can put this solution on YOUR website! Let us start over since you made a slight mistake near the end where you stopped.
 ---> (subtract 5 from both sides, then square each side)
 ---> (square of a square root is itself)
 ---> (use FOIL on the right hand side)
 ---> (combine like terms)
 ---> (subtract x+7 from each side)
 ---> (move equal sign to other side and combine like terms again)
 ---> (Now what two number are both positive or both negative and factors of 18 that add up to -11. We have the factor of 18 are in pairs: (1,18),(2,9),(3,6),(6,3),(9,2),(18,1), and in each pair either both are positive or both negative. We can see that -9-2=-11 and (-9)*(-2)=18)
So we see that factoring here was an easier option than the quadratic equation, and our answers appear to be x=2,9, but we can check to make sure they both work in the original equation: . Now notice that plugging in 2 for x does not work, because during the second step above we squared both sides to rid us of the square root, but if we didn't square both sides we would have had 3=-3, which can never happen. So our answer is x = 9.
Answer by freedom1(2) (Show Source):
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