Quick and Easy Question

[Bwbauer]

Hi guys, I am in 9th grade and need help with 1 simple problem I cannot wrap my head around.

The equation:x^2 - 3 = 2x ... We are supposed to describe to our teacher why this equation cannot be solved using the “Square Root Method/Principle”, since it can be solved using the quadratic formula and factoring.

 

[Dr.Peterson]

Presumably what is taught as "the method of square rooting" is to directly take the square root, in a case like x^2 = 5 or (x-1)^2 = 4. In those cases, there is only one x, namely the one being squared, so that when you take the square root of both sides, you will have something = constant and can solve.

In x^2 - 3 = 2x, the x appears both squared and unsquared, so the method (applied directly) would not have the right results, no matter how you first rearrange terms.

But you could instead "complete the square", making it look like (x-1)^2 = 4, and then take the square root. That would work. (And the quadratic formula is just the result of doing exactly this to the general form.) To my mind, the is "using the square root principle", but just as one step in a larger process. As I said, presumably that is not what is meant in the question.