Question

How do you solve `\frac { 3} { 2} ( x - 10) ^ { 2} = \frac { 1} { 2}`?

Answer 1

`x={(30+sqrt3)/3 , (30-sqrt3)/3}`

Explanation:

`3/2(x-10)^2=1/2`
Multiply both by 2
`3(x-10)^2=1`
`3(x^2-20+100)=1`
`3x^2-60+300=1`
`3x^2-60+299=0`

We know that if `ax^2+bx+c=0` then `x=(-b+-sqrt(b^2-4ac))/(2a)`

So `x=(-(-60)+-sqrt(60^2-4*3*299))/(2*3)`
`x=(60+-sqrt(3600-3588))/6`
`x=(60+-sqrt(12))/6`
`x=(60+-2sqrt3)/6`
`x=(30+-sqrt3)/3`

So, `x=(30+sqrt3)/3` or `x=(30-sqrt3)/3`