Question

Select the correct answer.

Solve the equation by completing the square.
0 = 4x2 - 64x + 192
OA. x= 4, 12
OB. x=-12, -4
x= -8,24
x = -24, 8

Answer 1

Option A) x=4,12 is correct.

The solution of the given quadratic equation is x=4,12

Explanation:

Given equation is in quadratic form

Given quadratic equation is

`0=4x^2-64x+192`

Rewriting the above equation

`4x^2-64x+192=0`

Now dividing the equation by 4 we get

`(1)/(4)(4x^2-64x+192)=(0)/(4)`

`x^2-16x+48=0`

For quadratic equation
`ax^2+bx+c=0`

solution
`x=(-b\pm√(b^2-4ac))/(2a)`

where a and b are coefficients of
`x^2` and x respectively, c is a constant

Here a=1, b=-16, c=48

`x=-((-16)\pm√((-16)^2-4(1)(48)))/(2(1))`

`=(16\pm√(16^2-192))/(2)`

`=(16\pm√(256-192))/(2)`

`=(16\pm√(64))/(2)`

`x=(16\pm 8)/(2)`

Therefore

`x=(16+8)/(2)` and
`x=(16-8)/(2)`

`x=(24)/(2)` and
`x=(8)/(2)`

`x=12` and
`x=4`

Therefore the solution of the given quadratic equation is x=4,12

Option A) x=4,12 is correct.