Question

Solve: 0 = 4x^2 - 8x - 5?

Answer 1

0 = 4x^2 - 8x - 5
0 = (2x+1)(2x-5)
(2x+1) =0 or (2x-5)=0
Can you solve it from here?

Answer 2

not really can you walk me through it?

Answer 3

Okay, first, do you know how to do factorization?

Answer 4

sort of

Answer 5

I know Greatest common factors but never really learned group factoring or poly/trionomial factoring

Answer 6

Oh... have you learnt quadratic formula?

Answer 7

nope

Answer 8

Then....Normally, how do you solve quadratic equation?

Answer 9

Guesstimate

Answer 10

Do you know how to do completing square?

Answer 11

dont you turn ax2 + bx + c = 0 to

a(x+d)2 + e = 0

Answer 12

Yes

Answer 13

I know the formats but not really how to convert it

Answer 14

So, let's use that method, shall we start?

Answer 15

sure

Answer 16

0 = 4x^2 - 8x - 5
5 = 4x^2 - 8x
Understand?

Answer 17

I thought it would be -5 not just 5?

Answer 18

Nope add 5 on both sides to the equation 0 = 4x^2 - 8x - 5.
0+5 = 4x^2 - 8x - 5 +5
5 = 4x^2 - 8x

Answer 19

alright got it

Answer 20

then what?

Answer 21

Take out common factor on the right side
5 = 4x^2 - 8x
5 = 4(x^2 - 2x)
Got it?

Answer 22

yea 2x is the common factor of 4 and 8 right?

Answer 23

Hmm.. Yes... But we need to complete square, so, keep it as x^2

Answer 24

alright

Answer 25

Since a^2-2ab+b^2 = (a-b)^2
now, a=x
So, we have x^2 -2xb + b^2
Compare this to the equation we have ( Consider the things inside the bracket first)
To complete square:
(x^2 - 2x) = x^2 -2x + (2/2)^2 - (2/2)^2
= x^2 -2x +1 -1
= (x-1)^2 -1

Answer 26

Got it so far?

Answer 27

lagged sorry

Answer 28

no worry. But I have to leave in 30 minutes. just a notice.
Tell me if you understand this step or not after you've finished

Answer 29

I don't completely understand this step

Answer 30

So, which one you don't know?

Answer 31

first 1

Answer 32

Can you copy that step?

Answer 33

Since a^2-2ab+b^2 = (a-b)^2
now, a=x
So, we have x^2 -2xb + b^2

Answer 34

a^2-2ab+b^2 = (a-b)^2 <- this is the identity for perfect square..Got it?

Answer 35

yea

Answer 36

Now compare the two, what do you observe?
a^2-2ab+b^2
(x^2 - 2x)

Answer 37

that ^2 is in both

Answer 38

So, we can say x ~ a , if we want to get the perfect square, what is the value of b required?

Answer 39

Hints: compare -2ab and -2x, take x=a as I've mentioned

Answer 40

-2x is common factor?

Answer 41

Yes, you can say so

Answer 42

ok

Answer 43

then what?

Answer 44

What is the value of b you get?

Answer 45

-2?

Answer 46

Nope...
-2ab = -2x
Put a=x
-2xb= -2x
b=1
Got it?

Answer 47

yea

Answer 48

So...
(x^2 - 2x) = x^2 - 2x +1 -1 Got it?

Answer 49

yep

Answer 50

(x^2 - 2x) = x^2 - 2x +1 -1 = (x-1)^2 -1
Got it?

Answer 51

Since (x-1)^2 = x^2 -2x +1

Answer 52

@Brad1996 ?

Answer 53

im back

Answer 54

sorry

Answer 55

yea i got it

Answer 56

1hr on 1 question :l

Answer 57

Back to the previous steps, we have
5 = 4x^2 - 8x
5 = 4(x^2 - 2x)

Put (x^2 - 2x) =(x-1)^2 -1 into 5 = 4(x^2 - 2x)
We'll get
5 = 4 [(x-1)^2 -1] Got it so far?

Answer 58

lol nearly finish :)

Answer 59

yep

Answer 60

Divide both sides by 4
5/4= 4 [(x-1)^2 -1] /4
5/4 = [(x-1)^2 -1]
Got it?

Answer 61

x = -1/2, 5/2

Answer 62

@SWAG Answer is not that important. The asker needs to know how to do it, instead of knowing the numbers for a single question

Answer 63

You showed him how to do it though

Answer 64

Haven't reached the last step. There's still possibility that the asker doesn't understand

Answer 65

@Brad1996 Do you understand the previous steps ?
Divide both sides by 4
5/4= 4 [(x-1)^2 -1] /4
5/4 = [(x-1)^2 -1]

Answer 66

yea

Answer 67

Add 1 to both sides.
5/4 +1= (x-1)^2 -1 +1
9/4 = (x-1)^2 <- Got it?

Answer 68

yep

Answer 69

Now take square root for both sides.
9/4 = (x-1)^2
x-1 = 3/2 or x-1 = -3/2

Note that \[\sqrt{y^2} = \pm y\]
Got it?

Answer 70

yea

Answer 71

Solve the 2 equations and you'll find x :) can you do it?

Answer 72

yep

Answer 73

What do you get for the answers?