Can someone please help me with this problem?

Select all of the solutions to x - 6 = -x². If there are no solutions, check the empty set.
-3
-2
2
3
{}

Question

Can someone please help me with this problem?

Select all of the solutions to x - 6 = -x². If there are no solutions, check the empty set.
-3
-2
2
3
{}

anonymous · Answer

I got -3 and 2 is this correct?

anonymous · Answer

Rearrange the equation to get
$$x^2 + x - 6 = 0$$
This is the standard form of a parabola used to find its "roots" or "solutions".
Then you can use either the quadratic formula or a slightly shorter method to find the solutions. In this case, a short method can be used as follows:
Ask yourself, what two numbers multiply together to equal -6 and add together to get 1 (which is the coefficient of the second term, x). When you've figured that out, you can factorise the equation in the form (x - a)(x - b) = 0, where a and b are the solutions.

anonymous · Answer

Yes, -3 and 2 are correct, and you can verify them both by putting them back into the equation - if the left hand side equals the right hand side when you put one of the numbers in, that number is a solution.