i need help understanding this problem?

Question

Solve the following equation.

1,200=200+700x-100x^2

 

x = _____ , _____

Answer 1

Group all like terms together.

First subtract 1,200 from each side of the equation.  Doing so, does not change the equality.

1,200 - 1,200 = 200 + 700x - 100x^2 - 1,200

then

0 = 700 x  - 100 x^2  - 1,000

Now device each side by 100.  Why 100?  So to simply the problem.

0 = 7x - x^2 -10

now place in a form you are familiar seeing and multiple all terms by -1.

 x^2  - 7x  + 10  = 0

Now solve for x. but before doing so, think of what two numbers, when multiplied together will give 10 but will also add up to -7.  Also, remember that a negative number times a negative number is a positive number so now we have.

(x - 5 ) (x - 2 ) = 0

Check this work with the FOIL method (First, Other, Middle, Last).

Now divide each side of the equation by (x - 5).

You get

x - 2 = 0  or x = 2

Now do the same with the other factor to get the other answer for x

So you have TWO solutions, x = 2 and x = ?

 

Hope I was helpful.  Please let me know.

 

 

Answer 2

it's easiest to start this problem by noticing that you can divide each term in the equation by 100.

 

after you divide each term by 100 the problem reduces to

 

12 = 2 + 7x - x²

 

Now, this looks easier!

 

It's typical with this type of problem to know you have to factor and solve, or you can use the quadratic formula.  In either case, you should get all terms on one side, equal to zero.

 

Since x² is negative on the right side, let's bring everything to the left side

 

12 + x²-7x-2 = 0

 

this simplifies to

 

x² - 7x +10 = 0

 

now you are looking for factors of +10 that will add to get -7.  Only 5 x 2 gives you 10 and if you add -5 and -2 you get -7.

 

So this factors as

 

(x-5)(x-2) = 0

 

solving each for 0

 

x - 5 = 0 gives you a value of x = 5

 

similarly x - 2 = 0 gives a value of x = 2.

 

Thus the solutions are 2 and 5

 

You can check:

 

first for 2:

 

200+700(2)-100(2)²= 200 + 1400 - 100 (4) = 1600-400 = 1200.  This checks as correct.

 

and now for 5:

 

200+700(5)-100 (5)²= 200 + 3500 - 100(25) = 3700 - 2500 = 1200.  This also checks

 

Thus the solutions are x = 2 and x = 5