[rcole23]

how can i take this


0.04 (1.6 - x) (2.4 - x) = 4 x2


and rearrange it into the form ax2 (squared) + bx + c = 0

??

any help appreciated.

[Astrokel]

Simple expansion?

[rcole23]

Simple expansion?

So would the next step be...


(0.064 - .04x)(0.096 - .04x) = 4x2 (squared)

[sjb]

Simple expansion?

So would the next step be...


(0.064 - .04x)(0.096 - .04x) = 4x²

No, there is no need to multiply both terms by 0.04. Can you multiply out the (1.6 - x) (2.4 - x)  terms?

[rcole23]

OK, I thought that maybe I would have to expand the brackets?  I am a little confused because the answer has to equal 0.

So, how about

0.04 (1.6 - x) (2.4 - x) = 4 x2 (multiply (1.6 - x) (2.4 - x) together)

0.04 * 3.84 - X2 (squared) = 4X2 (squared)

0.1536 - x2 = 4x2 

[rcole23]

OK getting closer I think.    I was reading up about expanding binomials and came up w/ this.

I used the FOIL method (first, outside, inside, last)

I please ask if someone can check up on my negative and positive signs?  I think I have made mistakes there.

0.04 (1.6 - x) (2.4 - x) = 4 x2

0.04 + 3.84 - 1.6x + 2.4x + x2 = 4x2

(.064 - .04x)(2.4 - x)

foil

.1536 - .064x - .096x + .04x2 = 4x2

.1536 - .064x - .096x + .04x2 - 4x2 = 0

.1536 - 0.16x - 3.96x2 = 0

[UG]

OK getting closer I think.    I was reading up about expanding binomials and came up w/ this.

I used the FOIL method (first, outside, inside, last)

I please ask if someone can check up on my negative and positive signs?  I think I have made mistakes there.

0.04 (1.6 - x) (2.4 - x) = 4 x2

0.04 + 3.84 - 1.6x + 2.4x + x2 = 4x2

(.064 - .04x)(2.4 - x)

foil

.1536 - .064x - .096x + .04x2 = 4x2

.1536 - .064x - .096x + .04x2 - 4x2 = 0

.1536 - 0.16x - 3.96x2 = 0

0.04 (1.6 - x) (2.4 - x) = 4x²
0.04(3.84 - 1.6x - 2.4x + x²) = 4x²
0.1536 - 0.064x - 0.096x + 0.04x² = 4x²
0.1536 - 0.16x + 0.04x² = 4x²
3.96x² + 0.16x - 0.1536 = 0

[rcole23]

Thank you, I am at work right now but will rework the math when I get home just to practice.  Only took me 12 hrs to find out how to do this question lol  , I will enjoy the answer...

[rcole23]

OK getting closer I think.    I was reading up about expanding binomials and came up w/ this.

I used the FOIL method (first, outside, inside, last)

I please ask if someone can check up on my negative and positive signs?  I think I have made mistakes there.

0.04 (1.6 - x) (2.4 - x) = 4 x2

0.04 + 3.84 - 1.6x + 2.4x + x2 = 4x2

(.064 - .04x)(2.4 - x)

foil

.1536 - .064x - .096x + .04x2 = 4x2

.1536 - .064x - .096x + .04x2 - 4x2 = 0

.1536 - 0.16x - 3.96x2 = 0

0.04 (1.6 - x) (2.4 - x) = 4x²
0.04(3.84 - 1.6x - 2.4x + x²) = 4x²
0.1536 - 0.064x - 0.096x + 0.04x² = 4x²
0.1536 - 0.16x + 0.04x² = 4x²
3.96x² + 0.16x - 0.1536 = 0

Actually how do yo umake the 0.16x and the 3.92x2 positive and the .1563 a negatitive???  This is the answer I am getting.  I am not sure of how or why in the last step you switched most of your signs.


0.04 (1.6 - x) (2.4 - x) = 4 x2

0.04 (3.84 - 1.6x - 2.4x + x2) = 4x2

.1536 - .064x - .096x + .04x2 = 4x2

.1536 - .064x - .096x + .04x2 - 4x2 = 0

.1563 - .16x - 3.96x2 = 0

rearranged...

-3.96x2 - .16x + .1563 = 0

[UG]

They're both the same 

-3.96x² - 0.16x + 0.1563 = 0 is the same as 3.96x² + 0.16x - 0.1536 = 0

[rcole23]

They're both the same 

-3.96x² - 0.16x + 0.1563 = 0 is the same as 3.96x² + 0.16x - 0.1536 = 0

Hmm I know it has been a few days but I still don't get this comment.  How is -3.96x2 the same as positive 3.96x2 and so on for the other answers?  When I factor the rearranged quadratic equation into my quadratic formula with negatives and possitives I would get toally different answers?

[UG]

No, when you solve for 'x' you should get the same two roots for 'x'
There are the same because all of the signs have been reversed.

Imagine this:
-15 + 6 -7 + 16 = 0

Now if you reverse all of the signs

15 - 6 + 7 - 16 what do you get? 

[Borek]

They have the same roots, but they are not identical when it comes to their plots/values taken - the one with +3.96x² has a lower bound and a minimum value, the one with -3.96x² has an upper bound and maximum value (for the same x).