Question

Let's say that the variable 'x' is definitely some negative number.

So if I wanted to solve:

\[x^2=4\]

I get:

\[\pm \sqrt{x^2} = \pm \sqrt{4} \\ \pm x = \pm 2\]

I would have to take the positive value of 'x' and the negative value of '2' to make this true...is it okay to only take a positive square root of one side of the equation and the negative square root of the other?

Answer 1

\[\sqrt{x ^{2}}=\left| x \right|\]

Answer 2

it would be \[x=\pm2\] as per me

Answer 3

So every time I write it out, I have to put \[\pm \sqrt{x^2} = \pm \sqrt{4} \\ \pm |x| = \pm2 \\ -|x| = -2\]?

And I have to solve the absolute value equation every time?

Answer 4

why \[\pm \sqrt{x ^{2}}???\]

Answer 5

Because when you take the square root of a number, you don't know if 'x' is positive or negative

Answer 6

so what......that doesnt mean we should take\[\pm \sqrt{x ^{2}}?\]

Answer 7

If you don't, then you only get the positive... \[x^2 = 4 \\ \sqrt{x^2} = \sqrt{4} \\ x = 2\]
But x can also be -2, so just only '2' is an incomplete solution

Answer 8

here after\[\sqrt{x ^{2}}=\sqrt{4}\]
\[\left| x \right|=2\]
\[x=\pm 2\]

Answer 9

Ohh, you solved the absolute equation. Okay