Rational Numbers.. Please help!?

Question

2x^2 - 5x + 11 = 2[(x - 5/4)^2 - 25/16 + 11/2]
= 2[(x - 5/4)^2 + 63/16]
= 2[(x- 5/4)^2 + 63/8

I understand the top line of this equation but the rest confuses me! Can someone explain how to get from 25/16 + 11/2 then to 63/16 and to 63/8 in the last line. Thanks!

Answer 1

Simple enough. You need to get a common denominator.

Just as 1/2 equals 2/4 equals 3/6 equals 4/8...
... 11/2 = 22/4 = 44/8 = 88/16

So adding -25/16 to 11/2 is the same as adding -25/16 to 88/16.
That gives you 63/16.

In the last line, you've multiplied the 63/16 by two, in order to get it out of the parentheses. That's 126/16, which simplifies to 63/8.

Hopefully that helps!

Answer 2

2x^2 - 5x + 11
= 2[x^2 - 5/2 x + 11/2]
= 2[(x - 5/4)^2 - (5/4)^2 + 11/2]
= 2[(x - 5/4)^2 - 25/16 + 11/2]
= 2[(x - 5/4)^2 + 63/16]
= 2(x- 5/4)^2 + 63/8

Note that (x - 5/4)^2 = x^2 - 5/2 x + (5/4)^2 = x^2 - 5/2 x + 25/16
The coefficients of x^2 and x are the same as that asked for. Only the constant is different; i.e 25/16 instead of 11/2.
So we have to subtract away this 25/16 and add the necessary 11/2.

Answer 3

ok
11/2 = 88/16, understand?
so -25/16 + 88/16 = 63/16 thats step one
Step two
they are factroing the two out of the fraction
63/16 = 63/(2*8) i think you are missing a bracket in your last line
should read 2[(x-5/4)^2]+63/8

Answer 4

i think the last equation should have been
(X-5/4)sq+63/8

Answer 5

.

2x^2-5x+11=2[x^2-(5/2) x-25/16 + 11/2]

=2x^2-5x-25/8+11
Q.E.D.

Answer 6

Oh my God, my head hurts X

Answer 7

you are missing a ] bracket in your last line, please type your questions in correctly!