Please help me solve the following problem.The difference of two numbers -21.3. Their product is -72.9. What are the numbers?

Let's represent the two numbers with the variables x and
y.

The difference of two numbers is -21.3.  Their product
is -72.9.  Write this information as equations, using x and
y.

x - y = -21.3

x * y =
-72.9

Now rewrite both equations with an isolated
variable.

x = -21.3 + y

x =
-72.9 / y

Using the substitution method, you can write this
equation.

-21.3 + y = -72.9 /
y

Multiply both sides of the equation by
y.

-21.3y + y^2 = -72.9

The
equation is quadratic, so lets rewrite it in
standard form.

y^2 - 21.3y + 72.9 =
0

Use the Quadatic Formula to
solve.

y = [-b `+-`
sqrt(b^2 - 4ac)] / 2a

[21.3 class="AM">`+-` sqrt(-21.3^2 - 4 * 1 * 72.9)] / 2 *
1

[21.3 `+-`
sqrt(453.69 - 291.6)] / 2

[21.3 class="AM">`+-` sqrt(162.09)] / 2

(21.3 +
12.7) / 2 = 17

(21.3 - 12.7) / 2 =
4.3

Now substitute them into the orginal equations to find
x.

x = -21.3 + y

x = -21.3 +
4.3 = -17

The two numbers are -17 and
4.3

Check:  their difference is -21.3... -17 - 4.3 = -21.3
check

Check:  their product is -72.9... -17 * 4.3 = -73.1
check

Notice that the product is a little off from what we
wanted.  This is because of the rounding that took place when we square-rooted 162.09 in
the quadratic formula.

Another way to
check:

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-30,1,-1,10,1,1,1,1,1,300,200,func,x+21.3,null,0,0,,,black,1,none,func,-72.9/x,null,0,0,,,black,1,none"/>

Notice
that the graphs intersect at (-17,
4.3)

Solution:  The two numbers
are -17 and 4.3