Question

The equation 2x^2-2x-180=0 can be written in the form (x+a)^2+b=0, where x,a and b are integers. Find the value of x,a and b.

Answer 1

well actually it cannot be written that way

Answer 2

bloody hell.

Answer 3

First remove the common factor 2:
x^2-x-90=0
Complete the squares:
(x^2-2(1/2)x+(1/2)^2) -(1/2)^2 -90=0
(x-1/2)^2-361/4=0
a=-1/2, b=-361/4
Proceed to solve for x
(x-1/2)^2=361/4
take square roots
(x-1/2) = +/- 19/2
x=1/2+19/2 or 1/2-19/2
=10 or -9

Answer 4

i am wondering where these questions come from. you can write it as
\[x^2-x-90=0\] or
\[(x-10)(x-9)=0\] or
\[(x-\frac{1}{2})^2-\frac{361}{4}=0\] but you cannot write it in the form
\[(x+a)^2+b=0\] where and b are integers!

Answer 5

mathmate has solved the problem for you if you want to solve for x.
but you will not find integers a and b that fit that bill. sorry

Answer 6

btw i made a typo it should be
\[(x-10)(x+9)=0\]

Answer 7

I guess the question should have said rational numbers instead of integers.

Answer 8

it should have just said "solve for x" and we would have been done in a couple steps. i don't know where these "a's and "b"s are coming from

Answer 9

I am learning how to complete the square and my teacher said that when completing the square you need to write the equation as either (x+a)^2+b or (px+a)^2+b.

Answer 10

well that is not in fact true. but in any case if you want to write it as
\[(x+a)^2+b=0\] it is certainly not the case that a and b are integers.

Answer 11

but it works though, when I re write the equation in that form. why didn't it work for this equation?

Answer 12

??