Question

Explain why the equation ( x - 4 ) ^2 - 28 = 8 has two solutions. Then solve the equation to find the solutions. Show your work.

Answer 1

Answer:

Step-by-step explanation:

(x-4)2-28=8

Two solutions were found :

x = 10

x = -2

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (x-4)^2-28-(8)=0

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-8x-20

The first term is,  x2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -20

Step-1 : Multiply the coefficient of the first term by the constant   1 • -20 = -20

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -8 .

     -20    +    1    =    -19

     -10    +    2    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  2

                    x2 - 10x + 2x - 20

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

                   x • (x-10)

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

                   2 • (x-10)

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

                   (x+2)  •  (x-10)

            Which is the desired factorization