Cool math fractal

math image

math image

pre-algebra help lessonsalgebra help lessonsprecalculus / calculus help lessonsmath anxiety survival guidegeometry math artmath and jigsaw puzzlesCoolmath booksother math stuff
math help lessonsmath practice problemsmath gamesmath dictionarygeometry trigonometry reference area
teacher's areaparent's areaCoolmath 4 kidsSpike's Game ZoneFinance FREAKTotally Stressed OutScience Monster
Coolmath Algebra
Solving Quadratic Equations Lesson 3 - Freaky Things That Can Happen   (page 1 of 3)
---- This algebra lesson explains the freaky things that can happen when you solve quadratic equations by factoring.

math image
Now available: Coolmath Algebra books! Part 1, Part 2 and Part 3 covering the Algebra you need from Algebra 1 through Precalculus Algebra (Beginning Algebra through College Algebra)

other Coolmath Books: Coolmath Precalculus Review (the math you really need to survive Calculus 1) and Math Survival Guide (How to conquer math and deal with math anxiety)
line
Graphing Calculator Scientific Calculator << a new window will open for these
line
We've been solving nice guys like

x^2 - 3x - 18 = 0
Notice that it's already set equal to 0.

So, what if the problem starts out like this?

x^2 - 3x = 18

Can we just factor and do the blob thing?

x ( x - 3 ) = 18

So x = 18 or x - 3 = 18 which gives x = 21

Are these the answers?  Check them!

x = 18: x^2 - 3x - 18 = 0 which gives ( 18 )^2 - 3 ( 18 ) - 18 = 0 which gives 324 - 54 - 18 = 0 ... No way!

Why didn't this work?

Think about our main idea"

If a * b = 0 , then a = 0 or b = 0

IT MAKES SENSE!

But, THIS is what we tried:

If a * b = 18 , then a = 18 or b = 18

WE CANNOT SAY THIS!

Uh.... What about

3 * 6 = 18 or 2 * 9 = 18 ?

There are a ton of things a and b can be other than 18.

So, when you start with something like

x^2 - 3x = 18

ALWAYS SET IT  = 0  FIRST. 
ALWAYS!

x^2 - 3x - 18 = 0

Finish it!

YOUR TURN:

Solve  x^2 + 7x = 170

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
line
Graphing Calculator Scientific Calculator << a new window will open for these
line

.....:::::::::::::::  HELP SUPPORT COOLMATH  :::::::::::::::.....
:::::::  link to us   :::::::   advertise with us  :::::::  why we have ads  :::::::

Thanks for visiting Coolmath.com
© 1997-2010 Coolmath.com, Inc.