Question

How do you solve the equation and identify any extraneous solutions for `x=sqrt(-7x+8)`?

Answer 1

I would square both sides and get:
`x^2=-7x+8`
`x^2+7x-8=0`
Solving using the Quadratic Formula you get:
`x_(1,2)=(-7+-sqrt(49+32))/2=(-7+-sqrt(81))/2`
`x_1=(-7-9)/2=-8`
`x_2=(-7+9)/2=1`

substituting back into our original expression we see that only `x_2=1` can be used.