Question

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

Answer 1

Answer:

Step-by-step explanation:

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,

√( x + 4/3)² = √ 0

= x + 4/3 = 0

x = - 4/3

Answer 2

Answer:

x=-4/3,-4/3

Step-by-step explanation:

$\sf\ {9x}^{2} + 24x + 16 = 0 \\ \\ \sf\ \implies: {9x}^{2} + (12x + 12x) + 16 = 0 \\ \\ \sf\ \implies: {9x}^{2} + 12x + 12x + 16 = 0 \\ \\ \sf\ \implies:3x(3x + 4) + 4(3x + 4) = 0 \\ \\ \sf\ \implies:(3x + 4)(3x + 4) = 0 \\ \\ \\ \tt\ \: 3x + 4 = 0 \\ \\ \boxed{\sf\ \implies:x = \frac{ - 4}{3} } \\ \\ \bf\red{x = \frac{ - 4}{3} \: and \: \frac{ - 4}{3} }$