So hmmm x²+6x+8=0
alrite.. let's do some grouping now
( x² + 6x + [?]²) + 8 = 0
notice above, we have a missing fellow in order to get a perfect square trinomial... hmm who would that be?
let's take a peek at the middle guy of the trinomial.. 6x.. hmmm let's factor it, 2*3*x, wait a minute! 2 * 3 * x... we already have x² on the left-side, since the middle term is just 2 * the square root of the other two terms, that means that the guy on the right, our missing guy must be "3"
alrite, let's add 3² then, however, bear in mind that, all we're doing is borrowing from our very good friend Mr Zero, 0
so if we add 3², we also have to subtract 3², let's do so
(x² + 6x +3² - 3²) + 8 = 0
(x² + 6x +3²) + 8 - 3² = 0
(x+3)²=3² - 8
(x+3)² = 1
The trick here is that both times, part of the weight is soup
and part of the weight is the empty metal can.
1/2 soup + MTcan = 5
1/3 soup + MTcan = 4
Before going any further, it will make it a lot easier later if we change
the fractions in both equations to a common denominator:
1/2 = 3/6
1/3 = 2/6
3/6 soup + 1 MTcan = 5
2/6 soup + 1 MTcan = 4
Subtract the 2nd equation from the 1st one:
1/6 soup = 1
Multiply each side by 6 : <u>1 soup = 6</u>
Substitute this in the first equation:
1/2 soup + 1 MTcan = 5
1/2 ( 6 ) + 1 MTcan = 5
3 + 1 MTcan = 5
Subtract 3 from each side: <u>1 MTcan = 2</u>
The empty can weighs 2.
All the soup it can hold weighs 6.
A full can of soup weighs (2 + 6) = <em><u>8</u></em>
1/2h+1-3/4h+4 --------Combine like terms
-1/4h+5
