Complete the square 4x^2-x = 0 Answers in book are 0,1/4 but I don't know how they got those answers. Help!

Answer 1

You start by simplifying the problem
4x^2 - x = 0
x(4x - 1) = 0
and then you put in values of x which will give you the answer.
If you put 0 into the equation it becomes
=0(4(0) - 1)
=0

and if you put 1/4 into the equation it becomes
= 1/4(4(1/4) - 1)
= 1/4 (1 -1)
= 1/4 (0)
= 0
Therefore the answers are 0 and 1/4

if there is something like x(x + #)
then 0 is one of the answers

You find the other one by just looking at inside of that particular brackets.
ie (4x - 1)
and you want it to equal 0
so 4x - 1 = 0
4x = 1
x = 1/4

Answer 2

The easiest way is to say
4 x^2 - x = 0
therefore
x * ( 4x - 1 ) = 0
therefore x = 0 or 4x-1 = 0
therefore x =0 or x = 1/4

Answer 3

4x^2-x=0
=>x(4x-1)=0
Therefore either x=0 or 4x-1=0
Hence x=0 or 1/4

Answer 4

4x^2 - x = 0

x ( 4x - 1 ) = 0

Either x = 0 or x = 1/4

Answer 5

you can further make 4x^2-x=0 into x(4x-1)=0

so the possible solution is either x=0
or 4x-1=0 which make x=1/4

so x= 0 and x=1.4 are the solutions

Answer 6

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Answer 7

4x^2 - x = 0

factor out x:
x(4x - 1) = 0

Set each factor = to 0:
x = 0

-------
4x - 1 = 0

add 1 to both sides:
4x = 1

divide both side by 4:
x = 1/4

Answer 8

4x^2 - x = 0

4(x^2 - (1/4)x) = 0
4(x^2 - (1/4)x + 1/64) = 4/64
4[x - (1/8)]^2 = 4/64
4[x - (1/8)]^2 = 1/18
(x - (1/8))^2 = 1/64

x - (1/8) = +/- 1/8

x = 1/8 +/- 1/8

Therefore, x = {1/8 + 1/8, 1/8 - 1/8}
x = {2/8, 0}
x = {1/4, 0}

Answer 9

4x^2-x=0
4x^2-x- (1/2)^2=0+(-1/2)^2
(4x-1/2)^2=1/4
(4x-1/2)=+- square root 1/4
(4x-1/2)= +-1/2
4X=1/2+1/2
4x= 1
x=1/4----------------------------1)
4x=1/2-1/12
x =0-------------------------------2)

Answer 10

The other's answers are right.. And I think.. It's easy.. You should try it by yourself first..

I bet you didn't try to finish it//