01f6d59a-c1df-4684-a35b-7fca590299ea
prompter
If 2x^2 is 4, what is x?
aa373e45-4a27-48e2-a06f-db696dec522b
01f6d59a-c1df-4684-a35b-7fca590299ea
assistant
We can solve for x by following these steps:

    Divide both sides of the equation by 2:

    2x^2/2 = 4/2

    Simplify the left side of the equation by canceling out the 2s:

    x^2 = 2

    Take the square root of both sides of the equation:

    √(x^2) = √2

    Note that we take the positive square root because we are looking for a real value of x.

    Simplify the left side of the equation by canceling out the square and square root:

    x = ±√2

So the solutions for x are x = √2 or x = -√2.
eac8d630-29c0-4e1b-9175-881806140fec
aa373e45-4a27-48e2-a06f-db696dec522b
prompter
Can you explain why its positive and negative √2 and not just √2?
3735bc8f-e2ac-41c0-8f2d-425957b395b0
eac8d630-29c0-4e1b-9175-881806140fec
assistant
Yes, I can explain why there are two solutions to the equation 2x^2 = 4.

When we take the square root of both sides of the equation x^2 = 2, we get:

|x| = √2

The absolute value symbol (|x|) indicates that the solution to the equation could be either positive or negative. This is because a positive number squared and a negative number squared both yield a positive result.

Therefore, there are two possible values of x that satisfy the equation 2x^2 = 4: x = √2 and x = -√2. Both values of x squared give a result of 2, which when multiplied by 2 gives 4.
cf926724-68f5-4e84-9247-eb19585ccfc8
3735bc8f-e2ac-41c0-8f2d-425957b395b0
prompter
What's the square root of -2?