What two numbers multiply two -90 and add up to three

Question

I need to know the answer the two factors that  multiply two -90 and add up to 3

 

Answer 1

I know this is not a grammar class, but you need to know the difference between, two, to, and too, as well as how to use them correctly.  :Two" is a number.  "To" indicates direction of an animate noun.  "Too" means as well, or to included something else.  The middle part of the problem should say "multiply to -90".

 

Now that we got that grammar lesson out of the way, lets solve this problem.

 

Let one number = x

Let the other = y

 

Using these variables, we can create equations.

 

xy = -90                eq1    ----> the numbers that multiply

x + y = 3               eq2    ---->  addition to three

 

 

Using the substitution method, we can substitute eq2 into eq1 to obtain an equation with only one variable.  From eq2, y = 3 - x

 

x(3 - x) = -90

 

-x² + 3x = -90

 

 

Move all terms to the right side of the equation.

 

0 = x² - 3x - 90

 

 

Factor using FOIL, if possible.  If you can't, then use the quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = -3

c = -90

 

Plug in these values in the formula.  Then accept the positive value of x.  The reason for this is because one number must be positive and the other must be negative.  Since the difference between x and y is positive.  x must be positive, whereas y will be negative.

 

 

Answer 2

 

Let's see:  let x,y be the two unknowns.

 

When you have two unknowns, that's a clue to look for two equations...

 

x + y = 3  (given)

xy = -90   (given)

 

Rearrange 2nd equation with x by itself (divide both sides by y):

    x = -90/y

 

Substitute this value for y in the 1st equation:

   (-90/y) + y = 3

 

Now: 

     -90  + y² = 3y    (multiplied both sides by y)

     y² - 3y -90 = 0   (subtracted 3y from both sides, rearranged terms on left)

 

I could not find integer factors that give the above quadratic, so I just 

used the formula:

 

                        -b ±√[b²- 4ac]

                y  =  -----------------

                               2a

 

With our values:

a = 1

b = -3

c = -90      

 

               y = 11.104686   (or  -8.104686)

 

(using x = 3 - y):

               x = -8.104686 

 

 

Check (we know they add to 3 because that's how we constructed x, so check multiplication part):      

               

                xy  = (-8.104686)(11.104686) = -90   (ok) 

 

Note that if we chose the negative y answer, it would've just given us x = 11.104868,  which would

just swapped values of x and y without affecting anything.