SOLUTION: (sub subject is Factoring) solve {{{49a^2-56a+16=0}}} please justify your answer thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (sub subject is Factoring) solve {{{49a^2-56a+16=0}}} please justify your answer thank you      Log On


   

Question 453363: (sub subject is Factoring)
solve 49a%5E2-56a%2B16=0
please justify your answer thank you
Found 3 solutions by mananth, ikleyn, MathTherapy:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
49a%5E2-56a%2B16=0

%287a%29%5E2-2%2A7a%2A4%2B%284%29%5E2
This is similar to the identity
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
%287a%2B4%29%5E2

Answer by ikleyn(53617) About Me  (Show Source):
You can put this solution on YOUR website!
.
(sub subject is Factoring)
solve 49a%5E2-56a%2B16=0
please justify your answer thank you
~~~~~~~~~~~~~~~~~~~~~~ 

49a^2 - 56a + 16 = 0.


Left side is   %287a-4%29%5E2.


So, this equation   49a^2 - 56a + 16 = 0  has the root  a = 4%2F7.     ANSWER

Solved.



Answer by MathTherapy(10719) About Me  (Show Source):
You can put this solution on YOUR website!
(sub subject is Factoring)

solve 49a%5E2-56a%2B16=0 
please justify your answer thank you

Another WRONG answer by the other person. 

49a%5E2+-+56a+%2B+16+=+0 is in the form: %28a+-+b%29%5E2+=+0, NOT %28a+%2B+b%29%5E2+=+0, as the other person states.
So, it should be %287a+-+4%29%5E2, NOT%287a+%2B+4%29%5E2.
Therefore, we get: 49a%5E2+-+56a+%2B+16+=+0
                         %287a+-+4%29%5E2+=+0
                      sqrt%28%287a+-+4%29%5E2%29+=+sqrt%280%29 ----- Taking square root of both sides
                          7a - 4 = 0
                              7a = 4
DOUBLE Roots/Solutions are located at highlight%28a+=+4%2F7%29