how do you solve this and simplify??? I"m DESPERATE!!! PLEASE HELP?

Question

http://i20.tinypic.com/b6yr8z.jpg

please help me.. i've been struggling with this for like an hour now...

i need to multiply those together and simplify...

thank you..

Answer 1

You need to be clear on exactly what it is you want to do (or are asking US to do).

a) If you want to WRITE DOWN THE ORIGINAL QUADRATIC EQUATION, the expression you've written is just the DIFFERENCE of two squares, (x - q)(x + q) = x^2 - q^2, where q is the second factor in each parenthetical term (regardless of sign!).

b) On the other hand, if all you want to do is to SOLVE the equation, it is ALREADY factorised! No FURTHER simplification is either POSSIBLE, OR NEEDED!

(Going from these two linear factors to a quadratic equation is in fact not SIMPLIFYING, but rather COMPLICATING the problem; it would be a RETROGRADE step!)

ALL you have to do is to set each of the two linear factors EQUAL TO ZERO, IN TURN! That will give you the TWO possible solutions, and you'll be DONE.

NOW, just DO it!

Live long and prosper.

Answer 2

here is the solution if you want to multiply this out , then simplify it...

by the way...

If you really only want the values of x, they are...
+ - 2a / ( - b - sqrt( b^2 - 4ac) ) .... as mentioned by others earlier ...

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SOLUTION:
you will get ...

x^2 - ( 4a^2) / ( - b - sqrt( b^2 - 4ac) )^2 = 0 ... when you multiply

now... ( - b - sqrt( b^2 - 4ac) )^2 is...

( -b)^2 + 2 ( -b) ( - sqrt( b^2 - 4ac) ) + ( - sqrt ( b^2 - 4ac ) )^2 = b^2 + 2b sqrt( b^2 - 4ac) ) + ( b^2 - 4ac) ]

Thus , we have:

x^2 - ( 4a^2) / [ b^2 + 2b sqrt( b^2 - 4ac) ) + ( b^2 - 4ac) ] = 0

simplifying...

x^2 - ( 4a^2) / [ 2b^2 + 2b sqrt( b^2 - 4ac) ) - 4ac ] = 0 ,
or

x^2 - ( 2a^2) / [ b^2 + b sqrt ( b^2 - 4ac) ) - 2ac ] = 0

there's not much other simplification to be done from here...

this equation can be solved, if you like, for x , by taking the square root, x = + - sqrt [ ( 2a^2) / [ b^2 + b sqrt ( b^2 - 4ac) ) - 2ac ] ], ... but this is more complicated than the previous answers for x, so I don't think you would want these.. ...

hope this is what you needed.....


edit ... IT MAY SEEM STRANGE FOR YOU TO BE ASKED TO MULTIPLY THESE THINGS OUT, BUT IF YOUR INSTRUCTOR ASKED YOU TO DO SO [ OR ASSIGNED THIS PROBLEM ], THEN HE / SHE HAD A REASON FOR ASKING YOU TO DO SO, SO IGNORE ANY COMMENTS TO THE CONTRARY THAT IT MAKES NO SENSE .....

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strange...... a thumbs down when I supplied the correct solution and I'm the only one who multiplied and then simplified as asked for.....? ... someone out there doesn't know their Mathematics, or how to read , since the asker did CLEARLY state they wanted to multiply it out and then simplify .....

Answer 3

This is an equation set equal to zero. If you are trying to solve for x you are home. Don't bother multiplying anything together. The equation is already set up for you to write down the answer. There are two solutions for x.

x = ±2a / [-b - √(b² - 4ac)]

Answer 4

it will be rather messy to work out the details here, but you could let m=x and let n=[2a/-b-sqrt(b^2-4ac)]

that way, you could express the equation as
(m-n)(m+n)=0
which is m^2-n^2
bring the equations into m^2-n^2 and work from there. it will be easier!

good luck!!

Answer 5

x^2 - (2a^2/ b^2 - 2ac)

IT is the difference of two squares. insanely simple problem

Answer 6

I like that you uploaded a picture of the problem. Can't help you, though, sorry...