# Algebra 2 – solving quadratic equations

Q: The length of a rectangle is 4 cm longer than the width. If the rectangle’s area is 45 cm², what is the width?

Explanation:  Call the width x.  Then, the length is x+4.

Area of a rectangle = (length)(width).

45 = x(x+4)

45 = x² + 4x

0 = x² + 4x – 45

Now, factor:

0 = (x + 9)(x – 5)

x = -9 or x = 5

Since a length can’t be negative, discard x = -9.  The only solution is x = 5.  Since ‘x’ is what we called the width, it is the answer to the question.  Just put the appropriate unit on it: 5 cm.

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