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Quadratic Formula

Q:  What is the quadratic formula?  When do I use the quadratic formula?


A:  When I was in 6th grade, I promised myself that I would never ever memorize the quadratic formula.  Well, unfortunately…. I know it by heart and have it tattooed to on my leg… Ok, just kidding about the tattoo part.

How do I type to the quadratic formula without and equation editor?  I will say it in words… I will attempt to type it… And then I will link to it on wiki so that you may see it in all of its glory:

THE QUADRATIC FORMULA:

If ax² + bx + c = 0, then…

x = “Negative b, plus or minus the square-root of b-squared minus four a-c all over two a”

x = [-b ± √(b² – 4ac)] / (2a)

Or view the quadratic formula written out on Wikipedia!

Therefore, if you have an equation of the form ax² + bx + c = 0, you can solve for x by using the quadratic formula (you can also solve it by factoring or completing the square, but we will save those for another day).

Let’s do an example:

Solve:  3x² = 2x + 7

Step 1:  Set equal to 0.

3x² – 2x – 7 = 0

Step 2:  Identify a, b and c.

a = 3, b = -2, c = -7

Step 3:  “Plug and Chug” into the Quadratic Formula

x = [-b ± √(b² – 4ac)] / (2a)

x = [-(-2) ± √((-2)² – 4(3)(-7))] / (2*3)

x = [2 ± √(4 + 84)] / 6

x = [2 ± √(88)] / 6

TADA.  This is the answer.  Now, there is some simplifying you may be able to do (if you know how to simplify radicals, etc..]

x = [2 ± √(88)] / 6

x = [2 ± 4√(22)] / 6

x = [1 ± 2√(22)] / 3

The most simplified.  Or, if you want a decimal… Plug it into a calculator!


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