SOLUTION: x-9 = the square root of x-3

Question 134607This question is from textbook Algebra 1
: x-9 = the square root of x-3 This question is from textbook Algebra 1

Found 2 solutions by solver91311, vleith:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Square both sides:

Add -x+3 to both sides:

Factor:
and , so:

or

Check:

, therefore 7 is an extraneous root introduced by squaring both sides of the equation at the start.

Exclude 7.

Why not say ? Because by convention is the positive root.

The solution set is {12}.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Given:
square both sides

x =12, x =7 are potential solutions.
Test them
x = 12 ==> 12-9 = sqrt(9) this is true so 12 works
x = 7 ==> 7-9 = sqrt(4) generally a sqrt for this type of problem is the positive root. If the negative root is acceptable, then this works too
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