Question

How do you solve `(2x-3)^2 = 8`?

Answer 1

`x = 2.914 or x= 0.0585`

Explanation:

Method 1

Find the square root of each side:

`(2x-3)^2 = 8`

`2x-3 = +-sqrt8`

Consider each root separately:

`2x-3 = sqrt8`

`x = (sqrt8+3)/2 = 2.914`

Or

`2x-3 = -sqrt8`

`x = (-sqrt8 +3)/2 = 0.0858`

Method 2

Find the square of the binomial:

`(2x-3)^2 =8`
`4x^2 -12x+9 -8 =0 larr` make equal to 0

`4x^2 -12x +1 =0`

Now using the quadratic formula

`x = (-b+-sqrt(b^2-4ac))/(2a)`

`x = (-(-12)+-sqrt((-12)^2-4(4)(1)))/(2(4)`

`x =(12+-sqrt(128))/(8)`

`x = 2.914 or x = 0.0858`