McGraw Hill Glencoe Algebra 1, 2012
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McGraw Hill Glencoe Algebra 1, 2012 View details
4. Solving Quadratic Equations by Completing the Square
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Exercise 9 Page 576

When we are given the area of a rectangle, we generally need to use the formula for the area of a rectangle. In this case we need to write expressions for the length, and width,

Verbal Expression Algebraic Expression
the length is more than the width
Now that we have an algebraic expression, we can substitute. Then, let's see where we can go from there.
Simplify
Now, we have a quadratic equation that is equal to zero. Let's look for two factors of that have a sum of Since is negative, the sign of the factors will be different. Furthermore, since is positive, the factor with the larger magnitude will be positive too.
Factors Sum of factors
We have found our factors that have a sum of Since our leading coefficient is we can use and directly as part of the factoring.
Let's set each factor equal to zero and solve for
Solve for
Since represents a measurement of distance, we can ignore the negative solution and say the width of the rectangle is To find the length, we can add to the width and get