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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
x-9=sqrt%28x-3%29

Square both sides:

x%5E2-18x%2B81=x-3

Add -x+3 to both sides:

x%5E2-19x%2B84=0

Factor:
-7%2A-12=84 and -7-12=-19, so:

%28x-7%29%28x-12%29=0

x=7 or x=12

Check:

7-9=sqrt%287-3%29
-2%3C%3E2, therefore 7 is an extraneous root introduced by squaring both sides of the equation at the start.

Exclude 7.

Why not say sqrt%284%29=-2? Because by convention sqrt%28x%29 is the positive root. -sqrt%284%29=-2

12-9=sqrt%2812-3%29
3=sqrt%289%29=3

The solution set is {12}.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28x-9%29+=+sqrt%28x-3%29
square both sides
%28x-9%29%5E2+=+x+-3
x%5E2+-+18x+%2B+81+=+x+-+3
x%5E2+-+19x+%2B+84+=+0
%28x-12%29%28x-7%29=0
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