Question

Solve: 0 = 4x2 − 8x − 5.

Answer 1

4x²-8x-5 = 0
x²-2x-5/4 = 0
(x -1)² - 1 - 5/4 = 0 {completing the square}
(x -1)² - 9/4 = 0
(x -1)² = 9/4
x -1 = ±√(9/4)
x = 1 ±√(9/4)
x = 1±(3/2)
x = 1+(3/2) or 1-(3/2)
x = 5/2 or -1/2

Answer 2

@simplybeyoutiful got any more question

Answer 3

i just dont really get how to do it

Answer 4

there are many ways of going this

Answer 5

i think this is the easiest way

Answer 6

oooppps i'm wrong it will factor

if you put 4 = 2*2 and -5 = -5 * +1

and combine these factors (one from each) to get -8 we can factor

2 * -5 + 2 * 1 = -8
giving
(2x - 5)(2x + 1) = 0

so 2x - 5 = 0
x = 5/2
or
2x + 1 = 0
x = -1/2

solution st is 5/2, -1/2

Answer 7

okay thank you, but @laxplayer how did you do it?

Answer 8

Okay i will show and ur welcome @simplybeyoutiful

Answer 9

okay thanks

Answer 10

Assume that your function can be written in the form
(ax+b)(cx+d)
= acx² +adx + bcx + bd
= (ac)x² +(ad+ bc)x + bd

Compairing this to 4x²-8x-5 = 0 shows that we want to find a,b,c,d such that
Ac = 4
Ad + bc = -8
Bd = -5

Letas assume a,b,c,d are all integers and that a > 0

From ac = 4 we have the following options
A = 1 and c = 4
A = 2 and c = 2
(we can ignore a = 4 and c = 1 as we could just rename the variable)

From
Bd = -5 we have the following options
B = 1 and d = -5
B = -1 and d = 5
B = 5 and d = -1
B = -5 and d = 1

So this gives us the following options
(x + 1)(4x - 5)
(x - 1)(4x + 5)
(x + 5)(4x - 1)
(x - 5)(4x + 5)
(2x + 1)(2x - 5)
(2x - 1)(2x + 5)
(2x + 5)(2x - 1) ******this is the same as two above so can be ignored
(2x - 5)(2x + 1) ******this is the same as two above so can be ignored


Now we can just expand each of these to see which one if right!

(x + 1)(4x - 5) = 4x² - 5x + 4x - 5 = 4x² - x - 5
(x - 1)(4x + 5) = 4x² + 5x - 4x - 5 = 4x² + x - 5
(x + 5)(4x - 1) = 4x² - x + 20x - 5 = 4x² + 19x - 5
(x - 5)(4x + 5) = 4x² + x - 20x - 5 = 4x² - 19x - 5
(2x + 1)(2x - 5) = 4x² - 10x + 2x - 5 = 4x² - 8x - 5
(2x - 1)(2x + 5) = 4x² + 10x - 2x - 5 = 4x² + 8x - 5

You should have spotted that the second to last one was right!
so
4x²-8x-5 = 0
Becomes
(2x + 1)(2x - 5) = 0

But for xy = 0 either x=0 or y=0 (or both)
So either
(2x + 1) = 0 → 2x = -1 → x = -1/2
Or
(2x -5) = 0 → 2x = 5 → x = 5/2

Answer 11

i think i might get it haha

Answer 12

@simplybeyoutiful hope this helps