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

Algebra ->  Radicals -> 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      Log On


   

Question 183287This question is from textbook Precalculus
: +sqrt%28+4-7x+%29+ = +sqrt%28+2x+%29+
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) About Me  (Show Source):
You can put this solution on YOUR website!
Are you certain that the equation is not sqrt%284-7x%29+=+sqrt%282%29%2Ax (the last "x" is NOT in the square root)

If so, then...


sqrt%284-7x%29+=+sqrt%282%29%2Ax Start with the given equation.


4-7x+=+%28sqrt%282%29%2Ax%29%5E2 Square both sides


4-7x+=+2x%5E2 Square sqrt%282%29%2Ax to get 2x%5E2


-2x%5E2-7x%2B4=0 Subtract 2x%5E2 from both sides and rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-2, b=-7, and c=4


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%28-2%29%284%29+%29%29%2F%282%28-2%29%29 Plug in a=-2, b=-7, and c=4


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%28-2%29%284%29+%29%29%2F%282%28-2%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%28-2%29%284%29+%29%29%2F%282%28-2%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--32+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%284%29 to get -32


x+=+%287+%2B-+sqrt%28+49%2B32+%29%29%2F%282%28-2%29%29 Rewrite sqrt%2849--32%29 as sqrt%2849%2B32%29


x+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%28-2%29%29 Add 49 to 32 to get 81


x+=+%287+%2B-+sqrt%28+81+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%287+%2B-+9%29%2F%28-4%29 Take the square root of 81 to get 9.


x+=+%287+%2B+9%29%2F%28-4%29 or x+=+%287+-+9%29%2F%28-4%29 Break up the expression.


x+=+%2816%29%2F%28-4%29 or x+=++%28-2%29%2F%28-4%29 Combine like terms.


x+=+-4 or x+=+1%2F2 Simplify.


So the possible answers are x+=+-4 or x+=+1%2F2


However, if we plug in x+=+-4, 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.


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Answer:

So the only solution is x+=+1%2F2

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