SOLUTION: Hi! Given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b. I find this one very difficult, so it would be lovely if you can help me. I´

Algebra ->  Functions -> SOLUTION: Hi! Given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b. I find this one very difficult, so it would be lovely if you can help me. I´      Log On


   



Question 894322: Hi!
Given that
x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.
I find this one very difficult, so it would be lovely if you can help me.
I´ve tried to solve it with quadratic equation and I have tried to split in to two equations.
Thank you!
Klara

Found 2 solutions by reviewermath, Okeke_Christian:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
Given that
x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.
Answer:
x%5E2+-+14x+%2B+a+=+x%5E2+%2B+2bx+%2B+b%5E2
Therefore,
2b = -14 and b%5E2+=+a
b = -7 and %28-7%29%5E2+=+a
highlight%28a+=+49%29 and highlight%28b+=+-7%29

Answer by Okeke_Christian(26) About Me  (Show Source):