Algebra is a branch of mathematics that is used in all walks of life, not only physics and math class. Algebra is used to solve many problems through mathematical relationships represented by equal signs. These relationships are called equations which contain symbols (typically letters from the alphabet) that represent unknown quantities. The equal sign shows that the quantities on either side have the same value

Note: In most equations a variable (alphabetic symbol) will have one corresponding value for a certain problem. In some cases a problem can have more than one corresponding value.

Our curious nature motivates us to try and understand that which is unknown. This said, variables represent unknowns in an equation. In the equation 2x + 7 = 15, x is the unknown. To solve this equation for the unknown the following rule can be used:

Any operation preformed on one side must also be preformed on the other side.

To check a solution put it back in to the original equation and simplify.

In an equation where there are two or more unknowns you can no longer find the solution with only one equation. In general for n unknowns you need n equations. First you must take one equation and solve it for "x". Then take it and replace it wherever the variable "x" appears in the second equation. Solve that equation for "y". Lastly take the value you obtained for "y" and insert it back into one of the original equations and solve for x. To check simply put the values you obtain for "x" and "y" back into on of the equations and simplify.

Quadratic equations appear frequently throughout math and physics because of the parabolic curves it can form.

In a quadratic equation the variables a, b, and c are usually given. When solving for x you use the quadratic formula.

The indicates that there are two solutions to the equation one where the (+) is used and one where the (-) is used.

Sometimes in physics you will find that only one of the two solutions is realistically possible. In this case you would discard the answer which is illogical. Also note that b² must be greater than 4ac for a real answer to result. In the even that b² is less than 4ac then there is no "real" solution.