Simplifying quadratic equations

cheergirl795

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Apr 13, 2011
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I need some help with simplifying some quadratic equations. They are all word problems. Here is one. Please Help!!!

The length of a photograph is 1cm less than twice the width. The area is 45squarecm. Find the dimensions of the photograph.

This is what I have so far:
w=width
w (2w-1) = 45
2w^2 - w = 45
2w^2 - w - 45 = 0

Now what????

Thanks
 
Simplify? You are done with that! Try solving.

Factoring?
Completing the Square?
Quadratic Formula?
Draw a pretty graph?

Let's see what you get.
 
cheergirl795 said:
2w^2 - w - 45 = 0

Now what?

Check to see whether or not this polynomial factors.

You could use the Discriminant Test for that.

A quadratic polynomial Ax^2 + Bx + C factors nicely, if its Discriminant is a perfect square.

The Discriminant is the expression B^2 - 4AC.

In your exercise, the Discriminant equals 361, and 361 is a perfect square (19^2).

Hence, you could factor the lefthand side of your equation above, and then solve for w. (I like the factoring-by-grouping method, but you could also try brute force using trial-and-error.)

Can you factor the quadratic polynomial in this exercise? 8-)

 
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