Question

Find the root of the following Quadratic Equation , if they exist , by the method of completing the square...
kindly explain in detail..
I will mark as brainliest...

Answer 1

completing square method -------

2x²-7x +3 = 0

divide by 2 in both sides

x² -7/2x +3/2 =0

x² -7/2x = -3/2

add both sides (7/4)²

x² -2(7/4)x +(7/4)² = -3/2 +(7/4)²

here you see ,
x² -2.(7/4)x +(7/4)² just like a²-2ab +b²
we know this formula ,
e.g (a -b)²
use this

(x -7/4)² = -3/2 + 49/16

(x -7/4)² = (-24+49)/16

(x-7/4)² = 25/16
take square root both sides

(x -7/4) = ±5/4

x = 7/4 ± 5/4

x = (7±5)/4

x = (7+5)/4 and (7-5)/4

x = 3 and 1/2

Answer 2

2x²-7x+3=0
divide each term with 2 
x²-7x/2 +3/2 =0

x²-7x/2 = -3/2

x² -2* x* 7/4 = -3/2 [ here in second term we multiplied divided with 2]
⇒x² - 2*x*7/4 + (7/4)² = (7/4)² -3/2[ adding both sides (7/4)²]
⇒(x-7/4)² = 49/16 -3/2
⇒(x-7/4)² = (49-24)/16
⇒(x-7/4)² = 25/16
⇒(x-7/4)² = (5/4)²
∴x-7/4 = + or - (5/4)
x= 7/4+5/4  or x= 7/4-5/4
x=12/4 or x= 2/4
x=3 or x=1/2