SOLUTION: {{{ sqrt (4x-11) =x-4 }}} Were supposed to square both sides. Take everything to one side and set it equal to zero. Then factor by reverse of foil.

Question 135817:
Were supposed to square both sides. Take everything to one side and set it equal to zero. Then factor by reverse of foil.
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:
Square both sides.
Subtract 4x from both sides.
Add 11 to both sides.
Factor.
Apply the zero products rule.
or , so...
or
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Square both sides:

Put everything on the left, zero on the right:

Multiply by -1 to get rid of the negative on the lead coefficient as an aid in factoring:

Reverse FOIL:
and , so:

That is all you say you were asked to do, but there really is more to this problem. Given that the factors of are , that means that if , then either or . That would lead us to believe that either or is a solution to the original equation. But...

If , then
Therefore 3 is NOT a solution of the original equation.

If , then
Therefore 9 IS a solution of the original equation.

The act of squaring both sides of the equation in the very first step caused us to introduce an extraneous root -- one that is not a solution of the original equation. So despite the fact that we ended up with a quadratic equation to solve, there is one and only one element to the solution set of , namely .
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