whitdiva23 wrote:

Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.

\(2 - x^ 2 = x^2 - 4x + 4\);

Re-arrange: \(2x^2 - 4x +2 = 0\);

Reduce by 2: \(x^2 -2x + 1 = 0\), which is the same as \((x−1)^2=0\), so \(x=1\).

How would one know when to reduce the equation as opposed to trying to solve a quadratic equation ax^2 +bx + c when a>1. For example factoring out the 2x^2?