Question

What method would be best to use 53=4(x-3)^2-11

Answer 1

x = 7 , -1

Explanation:

SOLUTION :-

`4(x-3)^2-11 = 53`

• Add 11 to both the sides.

`=> 4(x-3)^2-11+11=53+11`

`=> 4(x-3)^2 = 64`

• Divide both the sides by 4.

`=> (4(x-3)^2)/(4) = (64)/(4)`

`=> (x-3)^2 = 16`

• Root square both the sides.

`=> √((x-3)^2) = √(16)`

`=> x-3 = +4 \; or -4`

Here , x will have two values -

1)
`x-3 = 4`

`=> x = 4 + 3 = 7`

2)
`x - 3 = -4`

`=> x = -4 + 3 = -1`

VERIFICATION :-

When x = 7 ,

`4(x-3)^2 - 11 = 4(7 - 3)^2 - 11`

`= 4 * 4^2 - 11`

`= 4 * 16 - 11`

`= 64 - 11`

`= 53`

When x = -1 ,

`4(x-3)^2 - 11 = 4(-1 - 3)^2 - 11`

`= 4 * (-4)^2 - 11`

`= 4 * 16 - 11`

`= 64 - 11`

`= 53`