solve for x: 4x+6=x^2+5x
please help !

Question

anonymous · Answer

I will help you out.

anonymous · Answer

thanks!

anonymous · Answer

i think x=2 but I'm not sure

anonymous · Answer

Ok, in order to solve this, it needs to be in standard form of a quadratic, this is something in the form $$ax^2+bx+c=0$$ 
The first thing that you have to do with your equation is rearrange terms until it looks like that form. To do this, we subtract 4x and 6 from the left side. the result is:
$$0=x^2-x-6$$
Now we want to see if we can factor it, which is possible. 
You know it is going to be in the form of (x+    )(x-     ).
Factors of -6 that add up to -1??? , 3 and -2 work, so lets plug those in.

The factored form is then (x+3)(x-2)

The equation is now $$0=(x+3)(x-2)$$
Which is solved when EITHER of the two quantities on the right hand side are zero (anything multiplied by zero is zero! This makes the equation true, and is a solution)

This occurs when either (x+3) = 0 or when (x-2) = 0, so x must either be -3 or 2.

anonymous · Answer

Remember, you can always plug your solution back into the original equation to check it.

anonymous · Answer

Any questions?

anonymous · Answer

okay that makes sense i knew 2 was part of the answer but didn't know if that was the only answer..thanks so much for your help ! (:

anonymous · Answer

you are welcome, glad it helped