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Solving Quadratic Equations

Let and be the desired real numbers. Using the given information, we can write two equations, one for the sum of the numbers and one for the product of the numbers. We can solve this system of equations using the Substitution Method. First, let's isolate in the first equation and substitute it into the second equation.
The related quadratic equation can be written as Our next step is to solve the quadratic equation. We can do this by graphing. Let's begin by finding the axis of symmetry using the formula For our equation, and
Simplify
Next, we will make a table of values using values around the axis of symmetry which is

Now, we will plot the points and graph the equation that passes through the points.

It seems like the zeros of the equation are and Let's investigate if they satisfy the original problem. Since the numbers satisfy both requirements stated in the exercise we have found the numbers we are looking for, and they are and