Solve Each Equation by completing the square... b² - 20b + 100=9

Question

I do know that C=(b/2)

Answer 1

b² - 20b + 100 = 9

 

1) Take half of the coefficient of the middle term

     and square it. 

    (-20)/2 = -10

    (-10)² = 100

 

2) we already have the correct amount added

    after the b² - 20b to complete the square

    b² - 20b + 100 = (b-10)² so

 

(b-10)² = 9

 

3). take square root of both sides

    b-10 = ±√9

    b-10 = ±3

    b = 10 ± 3

 

b = {7, 13}

 

Check answers:

 

7² - 20(7) +100= 9

49 - 140 + 100 = 9

9 = 9

 

13² - 20(13) + 100 = 9

169 - 260 + 100 = 9

9 = 9

 

answers check as correct.