-4x - 6 = x^2 ( i think u have to use the qua. formula)

Question

-4x - 6 = x^2  ( i think u have to use the qua. formula)

radar · Answer

It is going to be a complex number with both real and imaginary components.$$x ^{2}-4x+6=0$$ using completing the square technique.$$x ^{2}-4x+4=-2$$
$$(x-2)^{2}=-2$$
$$x-2=\sqrt{-2}$$ Taking the square root of both sides
$$x=2+\sqrt{-2}$$
$$x=2+$$

anonymous · Answer

? wats the answer?

radar · Answer

You can also use the i which is the$$\sqrt{-1}$$
getting the final answer$$x=2+\sqrt{2}i$$

anonymous · Answer

oh i didnt learn imaginary #'s yet :P im in 8th grade algebra

radar · Answer

You may then leave it x=2+sqrt -2.  The quadratic formula would of also worked.

anonymous · Answer

hmmm the answer key says 2+sqrt10 and i got 4+sqrt10 :P

radar · Answer

Let me check my work, no I have worked it using completing the square and completing the square with same solution.  If I made an error maybe someone will point it out. (please) lol

radar · Answer

*i meant using the quadratic formula.

radar · Answer

elecengr was here earlier, maybe he can come up with the "approved" solution.

anonymous · Answer

how did u go from the first step to the second step?

anonymous · Answer

orig. problem to "first step"

anonymous · Answer

sry i gtg thanks for helping me (:

radar · Answer

That is the problem, I should of had a +4x, Please disregard the rest and start with$$x ^{2}+4x+6=0$$

radar · Answer

Do you see how I got that?

radar · Answer

added 4x + 6 to both sides.

radar · Answer

Now complete the square by.$$x ^{2}+4x + 4=-2$$ subtracting 2 from both sides.
$$(x+2)^{2}=-2$$ Now take the sq root of both sides$$x+2=\sqrt{-2}$$
$$x=-2+\sqrt{-2}$$

radar · Answer

Not the school book answer but different.  Hope this helps.