Question

Pls answer this question...

Answer 1

100-(x-5)^2
=100-(x^2-10x+25)
=100-x^2+10x-25
=-x^2+10x+75
=x^2-10x-75
=x^2-15x+5x-75
=x(x-15)+5(x-15)
=(x-15) (x+5)
x=15,-5

hope it helps you

Answer 2

 Step by step solution :

Step  1  :

 1.1    Evaluate :  (x-5)2   =  x2-10x+25 

Trying to factor by splitting the middle term

 1.2     Factoring  -x2+10x+75 

The first term is,  -x2  its coefficient is  -1 .
The middle term is,  +10x  its coefficient is  10 .
The last term, "the constant", is  +75 

Step-1 : Multiply the coefficient of the first term by the constant   -1 • 75 = -75 

Step-2 : Find two factors of  -75  whose sum equals the coefficient of the middle term, which is   10 .

     -75   +   1   =   -74     -25   +   3   =   -22     -15   +   5   =   -10     -5   +   15   =   10   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  15 
                     -x2 - 5x + 15x + 75

Step-4 : Add up the first 2 terms, pulling out like factors :
                    -x • (x+5)
              Add up the last 2 terms, pulling out common factors :
                    15 • (x+5)
Step-5 : Add up the four terms of step 4 :
                    (-x+15)  •  (x+5)
             Which is the desired factorization

Final result :

(x + 5) • (15 - x)