Solve the equation by completing the square.
0=4x^2-64x+192

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ((0 -  22x2) -  64x) -  192  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  -4x2 - 64x - 192  =   -4 • (x2 + 16x + 48)  

Trying to factor by splitting the middle term

3.2     Factoring  x2 + 16x + 48  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +16x  its coefficient is  16 .

The last term, "the constant", is  +48  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 48 = 48  

Step-2 : Find two factors of  48  whose sum equals the coefficient of the middle term, which is   16 .

     -48    +    -1    =    -49  

     -24    +    -2    =    -26  

     -16    +    -3    =    -19  

     -12    +    -4    =    -16  

     -8    +    -6    =    -14  

     -6    +    -8    =    -14  

     -4    +    -12    =    -16  

     -3    +    -16    =    -19  

     -2    +    -24    =    -26  

     -1    +    -48    =    -49  

     1    +    48    =    49  

     2    +    24    =    26  

     3    +    16    =    19  

     4    +    12    =    16    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  4  and  12  

                    x2 + 4x + 12x + 48

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+4)

             Add up the last 2 terms, pulling out common factors :

                   12 • (x+4)

Step-5 : Add up the four terms of step 4 :

                   (x+12)  •  (x+4)

            Which is the desired factorization

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer