The -6 to both sides and +16 to both sides at the beginning were a good start.

But then the +16 disappeared from one side.

The really dangerous part, though, is that they didn’t recognize that x^2 – 8x wasn’t the perfect square they were shooting for — does this mean that they’re not understanding that the whole point of this process is to get to a perfect square? Do they really think that (x – sqrt(8))^2 = x^2 – 8x?

And then a few more problems again at the end, where they confuse 10 with sqrt(10) and also drop the second solution.

What would happen if they were asked to check their final answer? What would they notice? Where in the process would they think something bad had possibly happened?

## One reply on “Completing the Square”

The -6 to both sides and +16 to both sides at the beginning were a good start.

But then the +16 disappeared from one side.

The really dangerous part, though, is that they didn’t recognize that x^2 – 8x wasn’t the perfect square they were shooting for — does this mean that they’re not understanding that the whole point of this process is to get to a perfect square? Do they really think that (x – sqrt(8))^2 = x^2 – 8x?

And then a few more problems again at the end, where they confuse 10 with sqrt(10) and also drop the second solution.

What would happen if they were asked to check their final answer? What would they notice? Where in the process would they think something bad had possibly happened?