SOLUTION: Solve or answer the questions regarding equations. Show work. Find the roots of 5sqrtx minus x = 6

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Question 981419: Solve or answer the questions regarding equations. Show work.
Find the roots of 5sqrtx minus x = 6

Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Asqrt%28x%29-+x=6
5%2Asqrt%28x%29+=+x%2B6

square both sides
25x=%28x%2B6%29%5E2
25x+=+x%5E2+%2B12x%2B36

x%5E2-13x%2B36=0
x%5E2-9x-4x%2B36=0

x%28x-9%29-4%28x-9%29=0
%28x-9%29%28x-4%29=0
x=9 OR 4

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of solving your problem, I'll solve one exactly in every
detail like your problem.  That is to prevent students from ignoring 
the work we do here and submitting only our answers.

So I'll do this one step by step which is exactly like your problem.

7sqrt%28x%29-x%22%22=%22%2212

Isolate the square root term:

7sqrt%28x%29%22%22=%22%2212%2Bx

Square both sides:

%287sqrt%28x%29%29%5E2%22%22=%22%22%2812%2Bx%29%5E2

49x%5E2%22%22=%22%22144%2B24x%2Bx%5E2

%220%22%22%22=%22%22x%5E2-25x%2B144

%220%22%22%22=%22%22%28x-9%29%28x-16%29

x-9%22%22=%22%22%220%22;  x-16%22%22=%22%22%220%22

x=9; x=16

We must always check problems for extraneous roots when we
have squared both sides:

Check x=9

7sqrt%289%29-9%22%22=%22%2212

7%283%29-9%22%22=%22%2212

21-9%22%22=%22%2212

12%22%22=%22%2212

So 9 is a solution:

Check x=16

7sqrt%2816%29-16%22%22=%22%2212

7%284%29-16%22%22=%22%2212

28-16%22%22=%22%2212

12%22%22=%22%2212

So 16 is also a solution.

Now do your problem exactly like this one.

Edwin