Question

Write the discriminant of the quadratic equation (x+5)^2=2(5x-3)

Answer 1

hope this helps you ...

Answer 2

Answer:

x 1 = 3

,  x 2 = − 1 2

Explanation:

Completing the square means that you want to write  

2 x 2 − 5 x − 3 = 0  

on the form  

( x − a ) 2 = b

First, let's get rid of the constant in front of the 2nd degree term:

x 2 − 5 2 x -3 2 = 0  

We want this on the form

( x − a ) 2 = b  

i.e.  x 2 − 2 a x + a 2 = b

Comparing term for term, we see that  

2 a = 5 2

, i.e.  

a = 5 4

( x − 5 4 ) 2 = x 2 − 5 2 x + 25 16

We, therefore, have

( x 2 -5 2 x + 25 16 ) − 25 16 − 3 2 = 0  

or

 ( x 2 − 5 2 x + 25 16 ) = 25 16 + 24 16 = 4916

( x − 5 4 ) 2 = ( 7 4 ) 2  

x − 5 4 = ± 7 4  x = 5 4 ± 7 4  

Therefore  

x 1 -54 + 7 4 = 3

x 2 = 54 − 7 4

= − 1 2