Solve the equation: $$\sqrt{3x-2} +2-x=0$$
I squared both equations $$(\sqrt{3x-2})^2 (+2-x)^2= 0$$
I got $$3x-2 + 4 -4x + x^2$$
I then combined like terms $x^2 -1x +2$
However, that can not be right since I get a negative radicand when I use the quadratic equation.
$x = 1/2 \pm \sqrt{((-1)/2)^2 -2}$
The answer is 6
Best Answer
You can't square the equation the way that you did.
What you did was essentially $$ \sqrt{3x-2}^2+(2-x)^2 = 0 $$ but it should be $$ \sqrt{3x-2}^2 = (x-2)^2 $$ which becomes $$ 3x-2 = x^2-4x+4 $$ Solve from there.
And generally, if you have an equation, you can't apply operations to only part of one side. The rule is that "what you do to one side, you do to the other". So if you square the left side, you square the right side. If you were to square the left side of your original equation, it would become $$ (\sqrt{3x-2}+2-x)^2=0^2 $$ which won't get you where you want to go (at least, not as easily - you can get there by using the original equation to substitute out the square root from that point).