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A quadratic equation is an equation in one variable with a squared exponent. All quadratic equations can be solved using a simple formula.

Difficulty Level: easy      Time Required: 5 - 10 minutes

1. Use multiplication to clear all parentheses in the equation. Work from left to right and start with the innermost set of parenthesis and work outwards. For example: if you have 5x(x+3) = (x - 1)(x + 2), you would clear parentheses from left to right. We get: 5x² + 15x = x² -x + 2x - 2.
2. Simplify both sides of the equation by combining like terms. Do this by adding the coefficients of like variable combinations (x and x² are different). For example, here the right side needs simplifying: x² - x + 2x - 2 is simplified by combining -x and +2x to get +x. The right side is now: x² + x - 2.
3. Move all terms to the left side by adding or subtracting the appropriate terms. There should only be a zero on the right when you are done with this step. In our example, we need to subtract x² and subtract x and add 2 to both sides. We get: 4x² + 14x - 2 = 0.
4. Call the coefficient of x²: a; the coefficient of x: b; and the constant: c. Here, a = 4, b = 14, and c = -2. Write these numbers down.
5. Square b (calculate b²). Here it is 196.
6. Calculate 4 times a times c. Here it is 4(4)(-2) = -36.
7. Subtract 4ac from b². Here is is 196 - (-36) = 232. Notice that when we subtract a negative, we are really adding.
8. Square root this number. Write it down. Here, the square root of 232 is not a whole number (approximately 15.232). We'll just call it 15.232.
9. Calculate -b + that square root and -b - that square root. Here, we calculate -14 + 15.232 and -14 - 15.232. That is 1.232 and -29.232.
10. Divide these two numbers by 2 times a. In this case, we divide them by 8 = 2(4). The quotients are: .154 and -3.654. These are your answers.
    

1. The variable doesn't matter. Here we used "x", but we could have used "y" or "a" or even a greek letter. The process is the same.
2. Some equations that have higher powers than 2 can be solved a similar way. They are called "quadratic-like" equations.
   

Related Features:

• Here's a two-part tutorial on solving quadratic equations. Part I: http://math.about.com/library/blalgebra10.htm
• Part II: http://math.about.com/library/blalgebra11.htm