Quadratic Formula?

Question

okay...

the question is: x^2+5=4x

This is how i did it:
a=1
b=-4
c=5

4+/-square((-4)^2-4(1)(5)) / 2(1)

4+/-square(16-20) / 2

4+/-square(-4) / 2

Now why are people saying to:

x = 4+/- sqrt(16-20) all over 2

Thus x = 2+/- sqrt (-4)/2

Why is the 4+/- turned into a 2+/-?

I know that ----- Square(-4) turns into 2i

so how so i get the answer?

Thank you very much!

Answer 1

ok haven't done this for a while but here goes

so we have
x^2+5=4x
bring it all to one side
x^2-4x+5=0

x=(-b+-SQrt(b^2-4ac))/2a
so for this equation a=1 b=-4 c=5

so x=(--4+-SQrt(-4^2-4*1*5))/2*1
x=(4+-SQ(16-20))/2
x=(4+-SQ(-4))/2
x=(4+-SQ(4i^2))/2
x=(4+-2i)/2
x=2+i or 2-i

place back into original equation for proof

(2+i)^2+5=4(2+i)
((2+i)*(2+i))+5=8+4i
4+4i+i^2+5=8+4i
i^2=-1
4+4i-1+5=8+4i
so 8+4i=8+4i
therefore 2+i is valid now for 2-i
(2-i)^2+5=4(2-i)
((2-i)*(2-i))+5=8-4i
4-4i+i^2+5=8-4i
9-4i+i^2=8-4i
i^2=-1
9-4i-1=8-4i
8-4i=8-4i
therefore 2-i is also avalid value for x
always remember to go back to the original equation to check your answers if they don't work out then you know you've done something wrong

now we place your answers into the original equation to check them
so for x=3i
3i^2+5=4*3i
i^2=-1
3*-1+5=12i
-3+5=12i
2=12i
i=2/12

and for x=i
i^2+5=4i
i^2=-1
-1+5=4i
4=4i
i=1
now we see that we have a real number as a solution to i seeing as i is the square root of -1 we see that the answers are incorrect as neither of the answers squared equals -1 so sorry to say 3i and i are incorrect
but if you compare my working to yours you may find your error

ok i think think the reason that people are sayin that it turns into a 2 is that they are dividing the 4 by the two on the bottom row
and then not expressing that it has been done so there equation should be

x = 2+/- (sqrt (-4)/2)

Answer 2

Okay, I'll assume that you understand it's square _root_, not square. The thing you're messing up is that the formula is not:
-b±√(b²-4ac)/(2a)
It is:
(-b±√(b²-4ac))/(2a)
Your use of the language "all over" in step 4 suggests that you know this, but are getting confused because you're not writing it out explicitly. If you do, it will become obvious that:
(-4±√(16-20))/2
(-4±√(-4))/2
-4/2±√(-4)/2
-2±√(-4)/2

All that's happening is that I broke the fraction into two fractions and simplified the one on the left. After this you would simplify as:
-2±2i/2
-2±i

And this would be your answer (unless your teacher requires you to explicitly write "x=-2+i or x=-2-i").

BTW, I hope you didn't see the first answer I put. I made a fairly embarrassing mistake there (which has since been fixed).

Answer 3

Well, you have applied the quadratic formula correctly. I think you may have written your original problem down incorrectly though. Are you sure it wasn't x^2 - 5 = 4x ?