Quadratic Equation
A quadratic equation is one where one of the terms is squared. A quadratic equation is of the form:
aX^{2} + bX + c = 0, where a, b, and c are integers.
Here are some quadratic equations:
X^{2} + 4X  45 = 0  In this equation, X = 5 because 5^{2} + (4)(5)  45 = 0.

Constants: a = 1, b = 4, c = 45

2 X^{2} 18 = 0  In this equation, X = 3 because 2 X 9  18 = 0

Constants: a = 2, b = 0, c = 18
Note: b = 0 because there is no X term

X^{2} + 4X = 45  This is the same equation as the first one, except that 45 appears after the equal sign. To get it into a standard form,subtract 45 from both sides of the equation to put it in the form X^{2} + 4X  45 = 0 
Constants: a = 1, b = 4, c = 45

Sometimes it's not so easy to find X. For these cases you need a formula to compute X given the constants (a, b and c) in the equation.
Here is that formula:
x = b ± √
b 2 
4 a c 2a

The _{±} ("plus or minus") means that there are 2 solutions for X, one using the positive (+) value of the square root and one the negative () value.

When you think about it, X^{2} = 25 has another solution: X =  5 because  5 x  5 = + 25 also.
If you apply this formula to our first equation: X^{2} + 4X  45 = 0, (a = 1, b = 4 and c =  45) you get:
X =  4 ± √
4 2 
(4) (1) (45) So: 2
X =  4 ± √16 +180 = 2
X =  4 ± 14 = 2
X =  2 ± 7 = + 5 or  9: A value of  9 also works because (9)^{2} 36 45 = 0 also!
OK, here's a problem for you! Solve for X:
2X^{2}  2X  24 = 0 a = ____ b = _____ and c = _____
X = ______
