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and
Since and , this means that .
Now, you have to solve for x, using the quadratic formula. Begin by moving the terms on the right side of the equation to the left side:

Now, in the quadratic form, , a = 2, b = -1, and c = -3. Substitute these values into the quadratic formula, as shown below.










OR

OR

OR

The solutions are x = -1 OR x = 3/2.

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We are trying to solve the following system of equations:
x + y = 5
x - y = -9
Notice that the "y" terms are opposite in sign so we can simply add the equations together, like this:
2x + 0y = -4
2x = -4
Divide both sides by 2: x = -4/2 = -2
Now, x = -2 so substitute into either equation. Since the first equation involves addition and it looks easier, let's go with this one. We have:
x + y = 5
-2 + y = 5
Add 2 to both sides:
-2 + 2 + y = 5 + 2
y = 7
The solution is: (-2, 7)

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We are trying to solve:
First, bring the terms on the right side of the equation to the left side by doing the opposite (add 14x and add 40 to both sides):

Now, try to factor the above expression. Since 40 = 10 * 4 and 10 + 4 = 14 (the middle term), the expression above factors into the following:
(x + 10)(x + 4) = 0
Next, we have x + 10 = 0 OR x + 4 = 0, so x = -10 or x = -4.
The solutions are -4 and -10.

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Begin by moving all the "x" and "y" terms together, like this:

Now move the "9" to the other side and factor by grouping:
+ = -9
For , factor out a "5":

And for , factor out a "-1":

(to make the number in front of the term a positive number):
-1
Next, complete the square for . Remember that you need to take 1/2 of the middle term (1/2*-6 = -3) and square that answer (-3*-3 = 9). Then add this number to the expression to complete the square:

Note that if you distribute the above expression out, you will get the following:
(This means you added 45 to the original expression, something you will need to do to the other side as well.)
Do the same thing for :
1/2 * 12 = 6
Square 6: 6 * 6 = 36
So, complete the square and get the following:
-1
Distribute and get:
Of course, you will need to add -36 to the other side as well.
In summary, we have added 45 and -36 to both sides of the original equation (and need to add these numbers to the right side as well):
+
Simplify:

+
Factor a "5" out of :
=
Factor a "-1" out of :
=
SO:

Since the right side of the equation equals 0, this conic section is not a hyperbola and cannot be graphed.