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quadratic equations help

ok i was doing a few quadratic equations examples for revision...and i came across some that im not totally sure how to do...can someone please explain??

one is:

solve this quadratic equation: x (x+4) = 0

the other one is:

rearrange into the form 'x^2 + bx + c = 0' then solve by factorising:

x + 4 - 21/x = 0

i hope thats clear enough...thanks (:

tiger~torah Mon 12/05/08 12:58

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squarebear
Mon 12/05/08
13:00

Just by looking at the first one tells me that x=-4.

-4 +4 = 0 and anything multiplied by 0 is 0.

piggling
Mon 12/05/08
13:05

It's a long time since I did algebra, but this is how it goes I think!

everything you do to one side you must do to the other.
So start by multiplying out the left side & you get x2 (don't know how to right squared) +4x = 0

Then take the 4x from both sides. (x2 = -4x)

Then divide both sides by x (x2/x = -4)

SO x = -4

Hope that helps.

Sorry don't remember how to do the other one!

jake-the-peg
Mon 12/05/08
13:05

er +4?

that'd be 32=0

think of it as x² + 4x =0 =0

it's -4 or 0

for the second

multiply both sides of the equation by x

gives x²+4x-21=0

which you should solve as normal

jake-the-peg
Mon 12/05/08
13:06

Oh sorry SB I see what you were saying now, thought you meant +/- 4
Duh

squarebear
Mon 12/05/08
13:07

No-one mentioned +4.

squarebear
Mon 12/05/08
13:08

Sorry Jake. Yes it just struck me as being blindingly obvious to be honest.

piggling
Mon 12/05/08
13:23

x + 4 - 21/x = 0

same principle

Muliply everything by x to get rid of the fraction & you get
x2 +4x - 21 = x
Then deduct x from each side
x2 +4x -x - 21 = 0
so
x2 +3x - 21 = 0

Hope that helps

jake-the-peg
Mon 12/05/08
14:18

don't thinkso piggling

x times 0 is 0 not x

piggling
Mon 12/05/08
14:26

Woops! Did say it was a long time since I've done algebra!!!

piggling
Mon 12/05/08
14:26

tho of course that's just basic maths, so no excuse other than my great age!

factor30
Mon 12/05/08
21:38

Multiply throughout by x:
x^2 +4x-21=0
so (x+7)(x-3)=0
so x= -7 or x=3

derrynoose
Thurs 15/05/08
20:27

Re x(x + 4) = 0
If the product of two items is 0 then one or the other is 0.
So, if x(x + 4) = 0, either x = 0 or x+4 = 0.
Thus x = 0 or x + 4 = 0.
Hence x = 0 or x = -4.
Answers can be checked by substituting each value into the original equation.

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