SOLUTION: Hello, #25 Square root of 2X + 3 = 2X - 3 Thank you, Lauren

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Question 76932: Hello,
#25
Square root of 2X + 3 = 2X - 3

Thank you,
Lauren

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

Square root of 2X + 3 = 2X - 3 

sqrt%282X%2B3%29=2X-3

Square both sides:

%28sqrt%282X%2B3%29%29%5E2=%282X-3%29%5E2

2X%2B3=%282X-3%29%282X-3%29

Use FOIL on the right

2X%2B3=4X%5E2-6X-6X%2B9

2X%2B3=4X%5E2-12X%2B9

Get 0 on the left by adding
-2X-3 to both sides

0=4X%5E2-14X%2B6

Divide every term by 2

0%2F2=%284X%5E2%29%2F2-%2814X%29%2F2%2B6%2F2

0=2X%5E2-7X%2B3 

Factor the right hand side:

0=%28X-3%29%282X-1%29

Set each factor = 0

0=X-3

3=X

That's one answer.

0=2X-1

1=2X

1%2F2=X

That's the other answer.

You MUST ALWAYS check
even-root equations for
extraneous answers:

Checking the answer x=3

sqrt%282X%2B3%29=2X-3

sqrt%282%283%29%2B3%29=2%283%29-3

sqrt%286%2B3%29=6-3
sqrt%289%29=+3
3=3

That checks, so the answer x=3 is a solution.

Checking the answer x=1/2

sqrt%282X%2B3%29=2X-3

sqrt%282%281%2F2%29%2B3%29=2%281%2F2%29-3

sqrt%281%2B3%29=1-3
sqrt%284%29=+-2
2=-2

That DOES NOT check, so the answer x=1/2
is NOT a solution.

The only solution is X=3

Edwin