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Coolmath Algebra
Solving Quadratics Lesson 5 - The Quadratic Formula (Quadranator)  
(page 3 of 4)
---- This algebra lesson explains how to solve quadratic equations using the quadratic formula.

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Here's one that doesn't factor:

Solve  x^2 + x - 1 = 0

a = 1 , b = 1 , c = -1
 

x = -b +/- sqrt( b^2 - 4ac ) / 2a = -1 +/- sqrt( ( 1 )^2 - 4 ( 1 ) ( -1 ) ) /( 2 ( 1) ) = -1 +/- sqrt( 1 + 4 ) / 2 = -1 +/- sqrt( 5 ) / 2

So x = -1 - sqrt( 5 ) / 2 or x = -1 + sqrt( 5 ) / 2

Yep -- these messy little buggers are the answers:

{ -1 - sqrt( 5 ) / 2 , -1 + sqrt( 5 ) / 2 }

If you were in a science or business class, you'd need to pop these into your calculator to get decimal approximations for these.  Since you may need to do this someday, we better practice this. Since all calculators are different, it won't do much good for me to tell you how to enter this in... So, you're on your own.  Here are the answers:

exact: { -1 - sqrt( 5 ) / 2 , -1 + sqrt( 5 ) / 2 }

decimal approximation: { -1.618 , .618 }

Find out which of these your teacher wants.

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
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