Question

How do you solve `x^2 – 3x = 7x – 2`?

Answer 1

`x= 5+-sqrt(23)`

Explanation:

`x^2-3x = 7x -2`

is equivalent (subtract `(7x-2)` from both sides) to
`x^2-10x+2 = 0`

Using the quadratic formula for roots
`color(white)("XXXX")` `x= (-b+-sqrt(b^2-4ac))/(2a)`
which in this case gives
`color(white)("XXXX")` `x= (10+-sqrt(10^2-4(1)(2)))/(2(1)`

`color(white)("XXXX")` `color(white)("XXXX")` `= 5+-sqrt(23`