Question

solve 4x^2-12x+9=0 using completing the square method​

Answer 1

Your choice to mark me the brainliest

In  

4

x

2

−

12

x

+

9

=

0

as niddle term  

−

12

x

is twice the product (with negative sign) of square roots of first (

s

q

t

(

4

x

2

)

=

2

x

) and third term (

√

9

=

3

,

it can be factorized using formula  

a

2

−

2

a

b

+

b

2

=

(

a

−

b

)

2

Hence  

4

x

2

−

12

x

+

9

=

0

⇔

(

2

x

)

2

−

2

×

3

×

3

x

+

3

2

=

0

or  

(

2

x

−

3

)

2

=

0

and hence  

2

x

=

3

or  

x

=

3

2

Answer 2

Step-by-step explanation:

$4 {x}^{2} - 12x + 9 = 0 \\ \\ {(2x)}^{2} - 2(2x)(3) + {(3)}^{2} - {(3)}^{2} = - 9 \\ \\ {(2x - 3) }^{2} - 9 = - 9 \\ \\ {(2x - 3)}^{2} = 0 \\ \\ 2x - 3 = 0 \\ \\ 2x = 3 \\ \\ x = \frac{3}{2}$

So the roots are

$\frac{3}{2} \: and \: \: \frac{3}{2}$

Hope it helps.