Question

solve the following equation by the method of completing the square 9x^2+24x+16=0

Answer 1

Heya!!!

Here's your answer,

9x² + 24x + 16 =0

divide whole equation by 9 ( coefficient of x2)

we get,

x² + 24x/9 + 16/9 = 0

transfer the c to right side

we get,
x² + 8/3x = - 16/9

Now third term ; [ 1/2 x coefficient of x ]²
= ( 1/2 x 8/3 )²
= ( 4/3)²

Now adding third term to both the sides,

we get,

x² + 8/3x + (4/3)² = -16/9 + (4/3)²
( x + 4/3 )² = -16/9 + 16/9
= ( x + 4/3)² = 0/9
= ( x + 4/3)² = 0
taking square root on both the sides,

we get,
root ( x + 4/3)² = root 0
= x + 4/3 = 0
x = - 4/3

Hope you like it

Answer 2

9x2+24x+16=0

A=9 b=24 c=16

=-b+/-√b2-4ac/2a

=-24+\-√(24)2-4(9)(16)/18

= -24+\-√576-576/18

= -24+\-√0/18

X=-4/3 or +4/3