Question

solve : x − 8 = √(-18x + 67)

Answer 1

start with \((x-8)^2=-18x+67\) solve the quadratic equation and don't forget to check your solution in the original equation

Answer 2

1 or -3

Answer 3

nope

Answer 4

x^2+64-16x=-18x+67
x^2+2x-3=0
(x-1)(x+3)=0

Answer 5

so there r 2 solutions

Answer 6

hmmm really?

Answer 7

if you square both sides of an equation, you can introduce extraneous solutions
we know \(-5\) is not a solution to \(x+1=4\) but if we square both sides, it is a solution to \((x+1)^2=16\)
by squaring, we have introduces an additional solution, namely \(-5\) to the original equation \(x+1=4\)

Answer 8

that is why you have to check both solutions after you square, to see if they work. \(-3\) is not a solution to
\[x-8=\sqrt{-18x+67}\]