Question

How do you solve the equation `3(x-3)^2+2=26`?

Answer 1

`x=3+-2sqrt(2)`

Explanation:

`3(x-3)^2=26`

`rarr 3(x-3)^2=24`

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

`rarr x^2-6x+9=8`

`rarr x^2-6x+1=0`

Applying the quadratic formula
`color(white)("XXX")x=(-(-6)+-sqrt((-6)^2-4(1)(1)))/(2(1))`

`color(white)("XxXX")=(6+-sqrt(32))/2`

`color(white)("XxXX")=(6+-4sqrt(2))/2`

`color(white)("XxXX")=3+-2sqrt(2)`