btw this isn't my homework, these are practice problem i need explained to me. solve x^3 = 4x?

Answer 1

Anytime you need to solve a polynomial equation that is higher than 1st degree, you take everything to one side. Set it equal to zero. And, then try to factor it.

x^3 - 4x = 0

x(x^2 - 4) = 0

x(x-2)(x+2) = 0

So, there are 3 answers: 0, 2, -2.

If you put them back into the original equation, you will see that they work.

Answer 2

First, x^3 = 4x is the same as x x x = 4x. Next, divide both sides by x (noting that since both sides contain x, one of the possible values for x is 0). You'll end up with x x = 4, which is the same as x^2 = 4. To solve this, take the square root of both sides:

sqrt( x^2 ) = sqrt( 4 )
x = sqrt( 4 )

So x = sqrt( 4 ), and the square root of 4 is either positive or negative 2. So x = +/- 2. But remember that x can also equal 0. So the answer would be one of three possibilities:

x = 0; x = 2; x = -2

Answer 3

This was one long explanation...

set the equation equal to 0.

so x^3 - 4x = 0 (Move all the terms on one side)

next, you want to factor out an x term so that you can simplify it to...

x (x^2 - 4) = 0 but you could simplify this even more right?

You always want to have no number in front of x^2... just makes life easier...
Then you are able to ask yourself what two numbers adds to 0 and is multiplied by -4...
(Remember it's x^2 +0x -4)
You can make a list of multiplied numbers if you like.
well
1 times -4 make -4; but 1 plus -4 equals -3.. and so on until you get

2 times -2 make -4; and 2 plus -2 = 0

Insert the numbers in correctly... The format must look something like this...

x (x+2) (x-2) = 0

(as a check only, not required to solve this type of problem) Just think that if you were to go backwards from this...

first (x times x) outer (x times 2) middle (-2 times x) and last ( -4)

Notice how 2x and -2x cancel.

so all you have left is x^2 - 4.. see how that works? This is just a check though..

Another note: sometimes the negative sign has to be in the proper place in order for you factor correctly...
remember the x too!

Back to the problem...
x (x+2) (x-2) = 0

so now we solve for x....

x= 0;

now (x+2 = 0)

move 2 to the other side so that you have...

x= -2

and do this for the other one too.

(x-2) = 0
(x= 2)

whew!

so X= 2, -2, 0
Add more to your question and tell me if you are confused about anything

Answer 4

1. x^3= x*x*x, x*x*x = 4x
2. Divide both sides by x, and you get x*x, or x^2=4
3. Take the square root of both sides. rt(x^2) = 2, rt(x^2) = -2, since square roots can be +/-.
4. Go back to the original problem (x^3 = 4x). If you substitute 0 for x, the equation still works.
5. So. x = -2, 0, 2

Answer 5

x^3=4x

we will transpose 4x to the left thus making it -4x

x^3-4x=0

we will get the common factor of x^3 and -4x so that we could factor them.the common factor is x.

x(x^2-4)=0

just remember that x^2-4 is always equal to (x+2)(x-2)

x(x+2)(x-2)=0
x=0 or x+2=0 or x-2=0
x=-2 x=2

the values of x are 0,-2 and 2.we can write it in the form S.S.{0,-2,2} with S.S. stands for solution set.

(there are three answers to the problem because the degree of the equation is 3.the degree of the equation could be obtained by simply looking for the biggest exponent in the equation.)

Answer 6

x^3 = 4x
=> x^3-4x =0 adding -4x on both sides
=>x(x^2-4) =0
=> x=0 or x^2-4 =0
=>x=0 or(x+2)(x-2) = 0
=> x=0 or -2 or +2

Answer 7

x^3 = 4x (Subtract 4x from both sides)
x^3 - 4x = 0
x(x^2 - 4) = 0
x = 0
x^2 - 4 = 0 (Add 4 to both sides)
x^2 = 4 (Take the square root of both sides)
x = +2 or -2

Therefore, x = 0, x = +2, x = -2

Answer 8

Both people that said to divide by x are wrong, because that discludes one factor.
Shift all terms to the left side
X^3-4X = 0
FACTOR out an X
X(X^2 - 4) = 0
Use your binomial properties to factor what's left in the parentheses
X(X+2)(X-2)=0
You thus get as an answer
X = 0, 2, -2

Answer 9

x^3=4x
divide both sides by x
x^2=4
x =the square root of 4
x=2

check the answer
x^3=4x -----subsitute 2 for x -----(2)^3=4(2) -------8=8

Answer 10

x^3=4x
x^3/x= 4x/x
x^2=4
square root of x^2= square root of 4
x=2