Question

Can someone explain how to solve this equation:
4x^2 +2x + 4?

Answer 1

"solve" is vague. what is it you are actually trying to do?

Answer 2

I need to understand how to find the value of x.

Answer 3

Hello

Answer 4

Hi Dan. Hi Amistre. It is an honor to be helped by two of OpenStudy's best helpers.

Answer 5

I think your equation is most likely
4x^2 +2x + 4 =0 or
4x^2 +2x + 4 = y
you have to find the x based on based on the given value for y

Answer 6

as is, there is no "equality" to it, so x is any value on its domain

Answer 7

Sorry, it is = 0. My bad

Answer 8

I am just starting to learn quadratics.

Answer 9

the simplest solution then is to apply the quadratic formula

have you learned the formula?

Answer 10

But I want to also understand how to solve it with the other non formula way. Do you have a strategy? If you want to use another example that is fine too.

Answer 11

Completing the square is the main way, that is where the quadratic formula comes from

Answer 12

I just made this one up. But I have noticed that there are people in my class, and my teacher - that seem to know how to group things etc

Answer 13

the strategy is something called completeing the square, that im sure dan will explain to you

Answer 14

Please do.

Answer 15

4x^2 +2x + 4 =0
okay
so completing the square means you are going to have to put it in this form
(ax+b)^2=c

Answer 16

Well, this has no real root.

Answer 17

can you expand the expression on the left and see what happens
(ax+b)^2=c

Answer 18

a^2x^ +b^2 + 2axb

Answer 19

4x^2 +2x + 4 =0
a^2x^ +2abx+b^2 = c
okay look here we must first make sure we need the criteria for the coefficients of x, the b^2 and c we can compensate for as they are just constants and we can add constants to both sides of the equation

Answer 20

so we know that a^2 = 4 and 2ab = 2

Answer 21

this means
a=2
and b=1/2

Answer 22

any questions so far?

Answer 23

That is pretty clever.

Answer 24

Thanks

Answer 25

Still with you. But I did rate you.

Answer 26

4x^2 +2x + 4 =0
we are going to rewrite the 4x^2+2x part now
(2x+1/2)^2 +4 = +1/4
i am adding the b^2 = 1/4 to both sides, the other 1/4 is coming from the expansion of the squared bracket

Answer 27

(2x+1/2)^2 = +1/4 - 4
=-3.75
now we can solve for x
2x+1/2 = +- sqrt(-3.75)
x=+-(sqrt(-3.75) - 1/2)/2
notice the + or - coming up at the squareroot point and also notice that negative value in the square root so your roots are imaginary in this case

Answer 28

okay thanks :) please click on that golden bell on top to rate me

Answer 29

if you understand this question