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Factoring Quadratics

Factoring Quadratics 1.21 - Solution

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We know that the area of the rectangle is square feet. The dimensions of a rectangle are its length and width. Recall that the area of a rectangle is length times width. We know that the of the table is one foot shorter than twice its width. Let's call the of the table The length can be written as We now have an equation with one variable. If we can solve for the width then we can find the length. Let's start by putting our equation in standard form.
Simplify
Now we can factor the right hand side of the equation so that we can apply the Zero-Product Property.
Factor
Now that the equation is in factored form, let's apply the Zero-Product Property.
Solve for
Rearrange equation
We can see that and However, recall that represents width. Since it doesn't make sense to have a negative value as a width, is the only correct value.