Solve the Equation 6x=9+x^2 Please.

Question

I don't even know what would be the first step. 

Answer 1

The first step is to get the equation in the form of <something> = 0.

If you subtract 6x from each side, you get this:

 

x^2 - 6x + 9 = 0

 

The next step is to factor the equation into the form (x +- a)(x +-b) = 0.

We know that a*b must equal 9, and we know that a+b must equal -6.

 

Therefore, we can conclude that a is -3 and b is -3.

 

The factors of this equation then look like this:

 

(x-3)(x-3) = 0

 

Since both factors are the same, there is only one answer for x, which is what will make x-3=0.

 

Therefore x = 3.