_______2x^2-8x=0?

Question

Please can you help me through the steps of solving this equation.

The equation reads two x squared, minus eight x, equals zero.

The question is a part of my math homework and I need the answer by 7:00 on 11/14/06. (don't mind the underscores in the problem they are just there because I need to have 10 characters in my question.

Answer 1

x(2x-8)=0

so 0 and 4 work for x

Answer 2

2x^2 - 8x =0
use reverse FOIL method (i dont know if that what they call it at your school)

FOIL means first,outside,inside,last i.e.:
_------_
(x+1)(x+1) first = ex times ex equals ex squared --> x^2

_---------_
(x+1)(x+1) outsides = ex times one (add it to term before)
--> x^2 + 1x

_--_
(x+1)(x+1) insides = one times ex --> x^2 + 1x + 1x

_-----_
(x+1)(x+1) last = one times one --> x^2 + 1x + 1x + 1

add it together --> x^2 + 2x + 1 = 0

reverse FOIL is this backwards, as needed in your case:

2x^2 - 8x + 0 = 0
set problem to three terms (the + 0 doesnt affect anything)

(x )(x ) --> (2x )(x )
use to pairs of parantheses to distribute the x^2. add a 2 in front of the first one to make it 2x^2 (as in the first step of FOIL)

(2x )(x+0)
the hard part is balancing the last numbers so that they equal the
first and last terms ( in this case -8x and 0)
so place 0 in front of x so no matter what the number in front of 2x is, the result of "last" in FOIL will be 0 making it:
_------_
(2x ?)(x+0) = 2x^2
_-----_
(2x ?)(x+0) = 2x^2 + 0

now you need a - 8 (like the one in the problem) in your answer so add that to the last piece of your equation:

(2x-8)(x+0) = 0

use FOIL to check your work:

(2x * x) + (2x * 0) + (-8 * x) + (-8 * 0) =>
2x^2 + 0 + -8x + 0 =>
2x^2 - 8x +0 = 0 is the same as 2x^2 - 8x = 0 so it was done right.

now finish the problem by finding x (in the case of FOIL, x is usually only two possibilities)-->
(2x-8)(x+0) = 0

set the problem into 2 chunks and solve for x in each:
(2x-8)=0 and (x+0)=0
2x-8=0 x+0=0
2x=8 x=0
x=8/2
x=4

x=4 or 0

so x can equal 4 or 0 in the original equation, and the equation will still balance:

2(0)^2 - 8(0) = 0?
0 - 0 = 0?
0 = 0 true

2(4)^2 - 8(4) = 0?
2*16 - 32 = 0?
32 - 32 = 0?
0 = 0 true

so the 2 possible answers are x=4 or x=0

:-)

Answer 3

Here's the original equation:

2x² - 8x = 0

First factor out the 2x:

2x(x - 4) = 0

According to the above expression, 2x = 0 and/or (x - 4) = 0.

This means that x = 0 and/or x = 4

When you plug the two numbers in, you see that they BOTH work.

Therefore, x = 0 AND x = 4

Answer 4

2x^2 - 8x = 0
Divide both sides of equation by 2 to get:
x^2 - 4x =0
Now factor out the x which is common to both terms to get:
x(x-4) = 0
Now set each factor = 0 getting two answers:
x=0 (answer 1)
x-4=0
x=4 (answer 2)

Answer 5

ok... now what do you see that's in common of the stuf on the left side?

THey all have the factor of 2x.
so 0 =2x * (2x^2-8x)/2x
0=2x(x-4)
Now, when you have that, what does x have to be for the stuff on the right to equal zero?

X has to be 0, or x has to be 4.
hence, x=0, or x=4

easy.

Answer 6

2x^2 - 8x = 0
2x(x - 4) = 0 ... First, take out 2x from each part...
This means that either 2x has to equal 0, or x - 4 has to equal 0.
So...
2x = 0 ... x = 0
x - 4 = 0 ... x = 4

So the answer is x = 0 or x = 4.

Answer 7

since 8 is divisible by 2 ( remainder is 0 ) take 2 common

2(x^2-4x)=0

Divide by 2 all throughout

X^2-4x=0

take x common

x(x-4)=0

therefore either x=0 or x-4=0
hence x=0 or x=4

Answer 8

2x^2-8x=0
2x^2=8x
2x=8
x=4