(solve using the quadratic formula)?

Question

x² + 6x + 8 = 0 (solve using the quadratic formula)

I cant figure out how to set this up, can someone please help.

Answer 1

okay...in your equation, find a,b,c

x^2....a=1
6x......b=6
8........c=6

find the two factors of c, that when multiplied together give you b

factors of 8 are: (1,8), (2,4), (-1, -8) and (-2, -4)

the factors (2 and 4) when added give you 6...therefore the solution is....
x^2 + 2x + 4x + 8 = 0
x(x+2) + 4(x+2) = 0
(x+2)[(x+4)]=0
(x+2)(x+4)=0

now going two different ways...
(x+2)=0/(x+4)
x=[0/(x+4)]-2
x=-2

OR

(x+4)=0/(x+2)
x=[0/(x+2)]-4
x=-4

let's put -2 in for x for the original equation to see if it works...

(-2)^2+6(-2)+8=0
4-12+8=0
12-12=0
0=0

let's put -4 in for x for the original equation to see if it works

(-4)^2+6(-4)+8=0
16-24+8=0
24-24=0
0=0

so x can be either -2 or -4

Now, to take a look at the equation to isolate x on one side...

x^2+6x+8=0
x^2+6x=-8
x(x+6)=-8
x=-8/(x+6)

let's see if -2 and -4 still work for x

-2=-8/(-2+6)
-2=-8/(4)
-2=-2

-4=-8/(-4+6)
-4=-8/(2)
-4=-4

So that proves that x can be either -2 or -4

Answer 2

you know the answer is going to be in the form of (x+a)*(x+b), right? that's just the way quadratics work.

and
(x+a)*(x+b) = x² + ax + bx + ab (that's just how you multiply them together, right?
and that is the same as
x² + (a+b)x + ab (just adding the ax+ bx together).


so now in your case you want:
a+b = 6 and a*b = 8

two variables and two equations can be solved algebraically, but you can probably see that the only pair that works is 2 and 4.

in other words
x² + 6x + 8 = (x+2)*(x+4) = 0

now solve for x... when you are multiplying two numbers to get 0, that means either one can be 0.. (0 times anything = 0).

so one answer is to say x+2 =0.... that is x = -2.
the other answer is to say x+4 = 0 ... that is x = -4.

so the two answers are -2 and -4

check your work by going back to the original equation

(-2)² + 6*(-2) + 8 = 4 - 12 + 8 and that is 0. good!
(-4)² + 6*(-4) + 8 = 16 - 24 + 8 and that is 0. good!

watch out for negative signs in these things, it is easy to get confused. and always go back and plug in your answers to the original equation to make sure it is right.

Answer 3

Here a=1, b=6 and c=8
The quadratic formula is (-b±/b²-4ac) divided by 2a where /=square root
Now simply put the values of a, b and c.
-6±/6.6-4(1)(8) divided by 2(1)
= -6 + /36 - 32 divided by 2 , -6 - /36 - 32 divided by 2
= -6 + /4 divided by 2 , -6 - / 4 divided by 2
= -6 + 2 divided by 2 , -6 - 2 divided by 2
= -4 / 2 , -8 / 2
= -2 , -4
Hence required answer is -2 , -4
Solution set = { -2 , -4 }


Thazz it....

Answer 4

Quadratic Formula

x = - b ± √b² - 4ac / 2a

x² + 6x + 8 = 0

a = 1

b = 6

c = 8

x = - 6 ± √(6)² - 4(1)(8) / 2(1)

x = - 6 ± √36 - 32 / 2

x = - 6 ± √4 / 2

x = - 6 ± 2 / 2

- - - - - - -

Solving for +

x = - 6 + 2 / 2

x = - 4 / 2

x = - 2

- - - - - - - -

Solving for -

x = - 6 - 2 / 2

x = - 8 / 2

x = - 4

- - - - - - - -s-

Answer 5

Quadratic formula method
x = [- 6 ± √(36 - 32)] / 2
x = [- 6 ± 2 ] / 2
x = - 2, x = - 4
Factor method
(x + 2).(x + 4) = 0
x = - 2, x = - 4

Answer 6

a = 1 , b = 6 , c = 8

x = [ -b +/- sqrt(b^2 - 4ac ]/2a
=[ -6 +/- sqrt ( 6^2 -4 (1)(8) ] / ( 2)
= [ - 6 +/- sqrt(4)]/2
= [ -6 +/- 2 ] / 2

x = ( -6 + 2)/2 or x = ( -6 - 2 ) / 2

x = -4/2 = -2 or x = -4
then x= -2 or x = -4

Answer 7

1st way:
(x + 2)(x + 4) = 0 (You have to factorise it)

Therefore:
x + 2 = 0......rearrange to get x = -2
x+ 4 = 0......rearrange to get x = -4

2nd way:
Substitute the letters in the formula:
a= 1
b= 6
c= 8
The quadratic formula is this:
(-b±/b²-4ac) divided by 2a
Therefore:
[-6±/6²-(4x1x8)] divided by (2x1)
-6±/4 divided by 2
(-6+2) divided by 2......................or (-6-2) divided by 2
-4 divided by 2 = -2......................or -8 divided by 2 = -4
therefore x= -2 or x= -4

Answer 8

Here's the setup:

a = 1, b = 6, c = 8.

x = [-b +- sqrt(b^2 - 4ac)]/2a, where +- means "plus or minus".

You should get a pair of real roots.

Answer 9

x=(-6+/- sqrt(36-32))/2
x=(-6+2)/2 and x=(-6-2)/2
x=-2 and x=-4