SOLUTION: {{{ sqrt( 4-7x ) }}} = {{{ sqrt( 2x ) }}} Hi, I have been squaring both sides to get rid of the radical signs: 4-7x = 2x. x = 4/9 is what I'm coming up with, but the answer ke

Question 183287This question is from textbook Precalculus
: =
Hi,
I have been squaring both sides to get rid of the radical signs: 4-7x = 2x. x = 4/9 is what I'm coming up with, but the answer key says x = 1/2. I'm missing something. Any help explaining this problem would be greatly appreciated.
Thanking you in advance,
Lynn Scott
This question is from textbook Precalculus

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Are you certain that the equation is not (the last "x" is NOT in the square root)

If so, then...

Start with the given equation.

Square both sides

Square to get

Subtract from both sides and rearrange the terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, if we plug in , the left side will have a negative number inside the square root.

Since you CANNOT take the square root of a negative number, this means that we must ignore this value.

====================================================================

Answer:

So the only solution is
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The answer key is wrong unless your posting is wrong.
--------------
Cheers,
Stan H.
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