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Teach me how to do Quadratic Equations

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2 Answers

When you say you want to learn to "do" quadratic equations, I take it to mean that you wish to learn to solve for the variable. Since you seem to be new at it, let's assume that you want help with some basic concepts that will help you move along toward the deeper concepts.
 
The format for quadratic equations is: ax² + bx + c = 0, in which x is not known, a, b, and c are constants, and a is not equal to zero. A quadratic equation is the product of two "roots," so we can use some simple logic & the algebra you already know to solve them.
 
A basic strategy is to factor the equation into its two roots, then use deduction to solve for the variable. For example:
 
x² + 2x + 1 = 0
(x+1)(x+1) = 0
 
So, x+1 is the only factor: x+1 squared yields this quadratic equation.
 
Now, if the product of the factors is zero, one of those factors must equal zero. Since there is only one factor, it must equal zero:
 
If (x+1)=0, then x=-1
 
Let's look at one with two different factors:
 
x² + 3x + 2 = 0
(x+2)(x+1) = 0
x+2=0 or x+1=0
x=-2 or x=-1
 
I used my understanding of the FOIL method to factor the equation, then I speculated that either factor could equal zero. In this case of two different factors, there will be two possible solutions for x.
 
FOIL means "First, Outer, Inner, Last". When we multiply polynomials, we use this order to compute the product accurately. In the case of (x+2)(x+1)=0, there are four items in a specific order: an x, followed by +2, another x, and +1. x is "First" & +1 is "Last", and the two together are "Outer". The "Inner" items are +2 & the other x. Let's multiply & see how it works:
 
(x+2)(x+1) = 0
x² +1x +2x +2 = 0 (next combine "like" terms)
x² + 3x + 2 = 0
 
Learn to reverse this process & you will know how to factor many quadratic equations. Some cannot be factored this way, but I assume you are not yet ready for those. As Robert indicated, this is a large & complicated topic that cannot be "taught" properly on this message system. Follow up on Robert's link & search also for other tutor's videos on WyzAnt.com. You will also find plenty of great math websites & teacher videos elsewhere, including YouTube. Good luck!

Comments

Nice intro to the factoring method.  I have one comment because I (and others) wish FOIL never existed.
 
FOIL is not a method.   It is certainly not a mathematical operation.
It is a mnemonic to help students who do not understand what to do, do the operations.  FIOL, LOIF, LFOI, or a number of other mnemonics based on those letters or other things would work just as well.
Also, it only works in a very specific case - a binomial times a binomial.  It does not work for multiplying a monomial and a binomial, multiplying a monomial and a trinomial, a binomial and a trinomial, two trinomials, etc. Instead students should learn the method - to multiply every term in the first times every term in the second.
Fair enough, Robert! Hopefully Daniel will get whatever help he needs.