what is x if 2x squared equals x squared -1?

2x² = x² - 1

First, subtract x² from both sides.

x²= -1

Then take the square root of both sides.

so $${\mathtt{x}} = {\sqrt{-{\mathtt{1}}}}$$ and $${\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{-{\mathtt{1}}}}$$

But in real numbers, you cannot have the square root of a negative number. So instead, there is this number, $${i}$$ , the imaginary number.

$${i}$$ by definition is the square root of -1

So x = i or x = -i